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Math Problems
Grade 6
Area of quadrilaterals and triangles: word problems
You want to know how many stories a skyscraper is, knowing the angle to the
5
th
5^{\text{th}}
5
th
floor, and the angle to the top floor.Find thr length of
x
x
x
if the smaller angle is
3
0
∘
30^\circ
3
0
∘
angle and the larger angle is
6
0
∘
60^\circ
6
0
∘
angle
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13
13
13
.
\newline
In the diagram,
P
P
P
is the point of intersection of the curves
y
=
e
2
x
y=\mathrm{e}^{2 x}
y
=
e
2
x
and
y
=
e
2
−
x
y=\mathrm{e}^{2-x}
y
=
e
2
−
x
.
\newline
(i) Find the
x
x
x
-coordinate of
P
P
P
.
\newline
Hence evaluate, correct to two decimal places,
\newline
(ii) the area of the shaded region,
\newline
(iii) the area of the region bounded by the two curves and the
y
y
y
-axis.
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Question
1
1
1
: (
3
3
3
Marks)
\newline
The table below shows the
C
O
2
\mathrm{CO}_{2}
CO
2
emissions (tonnes per capita) for the years
2014
2014
2014
and
2020
2020
2020
for the
28
28
28
countries in the European Union.
\newline
\begin{tabular}{|l|c|c|}
\newline
\hline \multirow{
2
2
2
}{*}{ European Union } & \multicolumn{
2
2
2
}{c|}{ CO
2
2
2
emissions (tonnes per capita) } \\
\newline
\hline Country Name &
2014
2014
2014
&
2020
2020
2020
\\
\newline
\hline Austria &
6
6
6
.
87
87
87
&
6
6
6
.
73
73
73
\\
\newline
\hline Belgium &
8
8
8
.
33
33
33
&
7
7
7
.
23
23
23
\\
\newline
\hline Bulgaria &
5
5
5
.
87
87
87
&
5
5
5
.
39
39
39
\\
\newline
\hline Croatia &
3
3
3
.
97
97
97
&
4
4
4
.
14
14
14
\\
\newline
\hline Cyprus &
5
5
5
.
26
26
26
&
5
5
5
.
38
38
38
\\
\newline
\hline Czech Republic &
9
9
9
.
17
17
17
&
8
8
8
.
22
22
22
\\
\newline
\hline Denmark &
5
5
5
.
94
94
94
&
4
4
4
.
52
52
52
\\
\newline
\hline Estonia &
14
14
14
.
85
85
85
&
7
7
7
.
88
88
88
\\
\newline
\hline Finland &
8
8
8
.
66
66
66
&
7
7
7
.
09
09
09
\\
\newline
\hline France &
5
5
5
.
08
08
08
&
4
4
4
.
24
24
24
\\
\newline
\hline Germany &
8
8
8
.
89
89
89
&
7
7
7
.
69
69
69
\\
\newline
\hline Greece &
6
6
6
.
18
18
18
&
5
5
5
.
01
01
01
\\
\newline
\hline Hungary &
4
4
4
.
27
27
27
&
5
5
5
.
00
00
00
\\
\newline
\hline Ireland &
7
7
7
.
31
31
31
&
6
6
6
.
73
73
73
\\
\newline
\hline Italy &
5
5
5
.
27
27
27
&
5
5
5
.
02
02
02
\\
\newline
\hline Latvia &
3
3
3
.
50
50
50
&
3
3
3
.
59
59
59
\\
\newline
\hline Lithuania &
4
4
4
.
38
38
38
&
5
5
5
.
07
07
07
\\
\newline
\hline Luxembourg &
17
17
17
.
36
36
36
&
13
13
13
.
06
06
06
\\
\newline
\hline Malta &
5
5
5
.
40
40
40
&
3
3
3
.
61
61
61
\\
\newline
\hline Netherlands &
9
9
9
.
92
92
92
&
8
8
8
.
06
06
06
\\
\newline
\hline Poland &
7
7
7
.
52
52
52
&
7
7
7
.
92
92
92
\\
\newline
\hline Portugal &
4
4
4
.
33
33
33
&
3
3
3
.
96
96
96
\\
\newline
\hline Romania &
3
3
3
.
52
52
52
&
3
3
3
.
72
72
72
\\
\newline
\hline Slovak Republic &
5
5
5
.
66
66
66
&
5
5
5
.
63
63
63
\\
\newline
\hline Slovenia &
6
6
6
.
21
21
21
&
6
6
6
.
04
04
04
\\
\newline
\hline Spain &
5
5
5
.
03
03
03
&
4
4
4
.
47
47
47
\\
\newline
\hline Sweden &
4
4
4
.
48
48
48
&
3
3
3
.
83
83
83
\\
\newline
\hline United Kingdom &
6
6
6
.
50
50
50
&
4
4
4
.
85
85
85
\\
\newline
\hline & & \\
\newline
\hline
\newline
\end{tabular}
\newline
(Table
1
1
1
)
\newline
3
3
3
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12
12
12
)
A
B
C
D
A B C D
A
BC
D
is a square. The length of
B
C
B C
BC
is
3
3
3
times the length of
E
B
E B
EB
.
\newline
a) What fraction of square
A
B
C
D
A B C D
A
BC
D
is the shaded part? (Hint: Draw lines to divide
A
B
C
D
A B C D
A
BC
D
into equal parts.)
\newline
b) If
E
B
=
3
c
m
E B=3 \mathrm{~cm}
EB
=
3
cm
, find the area of the unshaded part.
\newline
3
×
3
=
9
9
×
9
=
81
3
×
9
÷
2
=
\begin{array}{l} 3 \times 3=9 \\ 9 \times 9=81 \\ 3 \times 9 \div 2= \end{array}
3
×
3
=
9
9
×
9
=
81
3
×
9
÷
2
=
\newline
Ans: a)
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Estelle B
240
240
240
\newline
Ali |
240
240
240
\newline
You
\newline
240
240
240
\newline
Mookyungs
246
246
246
\newline
Almaa M
247
247
247
\newline
Use the net below to calculate the surface area of this rectangular prism.
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The figure below is a triangular prism. Ahswer the question(s) for your elass, show vour work:
\newline
Af Crases:
\newline
Pe-Algebra:
\newline
he volume of the flgure is g
60
60
60
int, What is the surtace area?
\newline
Bebra:
\newline
co surface area of the three rectangles is S
40
40
40
in?, What is the lume?
\newline
ometry:
\newline
surface area of the figure is
756
i
n
2
756 \mathrm{in}^{2}
756
in
2
, What is the volume?
\newline
20
20
20
.
5
5
5
\newline
Answer:
\newline
Surface Area
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June
232
H
232 \mathrm{H}
232
H
\newline
Overview
\newline
Question Progress
\newline
Exam Paper Progress
\newline
Grade For This Paper
\newline
29
/
80
29 / 80
29/80
Marks
\newline
u
3
3
3
3
3
3
.
\newline
15
15
15
\newline
6
6
6
\newline
T.
\newline
Here is a rectangle and a triangle.
\newline
All measurements are in centimetres.
\newline
The area of the triangle is
12
c
m
2
12 \mathrm{~cm}^{2}
12
cm
2
greater than the area of the rectangle.
\newline
Work out the value of
x
x
x
.
\newline
Optional working
\newline
x
=
x=
x
=
\newline
Answer
\newline
Total marks:
4
4
4
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Narne
\newline
Decompose Fractions into Sums
\newline
Model with Mathematics Look at the list of the names of the months of the year.
\newline
- Draw a visual model to show the fraction of the names of the months that contain the letter
y
y
y
.
\newline
\begin{tabular}{|l|l|}
\newline
\hline Lanuary & July \\
\newline
\hline February & August \\
\newline
\hline March & September \\
\newline
\hline April & October \\
\newline
\hline Mlay & November \\
\newline
\hline June & December \\
\newline
\hline
\newline
\end{tabular}
\newline
- Write an addition equation to model the fraction as a sum of the fractions representing each month.
\qquad
\newline
Write the fraction as a sum of unit fractions. Numerator is
1
1
1
.
\newline
[
2
2
2
]
2
6
=
\frac{2}{6}=
6
2
=
\qquad
[
3
3
3
]
4
5
=
1
5
\frac{4}{5}=\frac{1}{5}
5
4
=
5
1
\newline
(4.)
3
8
=
1
8
\text { (4.) } \frac{3}{8}=\frac{1}{8}
(4.)
8
3
=
8
1
\newline
\qquad
\newline
\qquad
\newline
\qquad
\newline
5
5
5
(
8
8
8
) Model with Mathematics Marlon threw a bowling ball twice and knocked down a total of
6
6
6
pins. Shade the visual fraction models to show two ways he could have knocked down the
6
6
6
pins on the two throws. Then model each with an equation.
\newline
Write the fraction as a sum of two fractions.
\newline
Module
14
14
14
* Lesson
1
1
1
\newline
P
1
1
1
as
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Substitute
s
=
3
s=3
s
=
3
. Area,
A
=
b
h
A=b h
A
=
bh
A
=
3
2
=
9
A=3^{2}=9
A
=
3
2
=
9
Substitute
b
=
5
b=5
b
=
5
and
h
=
2
h=2
h
=
2
.
A
=
5
×
2
=
10
A=5 \times 2=10
A
=
5
×
2
=
10
The area is
9
m
2
9 \mathrm{~m}^{2}
9
m
2
. The area is
10
c
m
2
10 \mathrm{~cm}^{2}
10
cm
2
.
\newline
Check
\newline
1
1
1
. Find the perimeter and area of each figure.
\newline
a)
\newline
−
2.0
k
m
=
2
(
=
Perimeter
=
\begin{array}{r} -2.0 \mathrm{~km}=2( \\ = \\ \text { Perimeter }= \end{array}
−
2.0
km
=
2
(
=
Perimeter
=
\newline
+
+
+
\qquad
\newline
Perimeter
A
=
b
h
A=b h
A
=
bh
0
0
0
\qquad
\newline
b)
\newline
P
=
2
(
b
+
h
)
P=2(b+h)
P
=
2
(
b
+
h
)
\newline
A
=
b
h
=
\begin{aligned} A & =b h \\ & = \end{aligned}
A
=
bh
=
\newline
\qquad
A
=
b
h
A=b h
A
=
bh
3
3
3
\qquad
\newline
=
=
=
\newline
\qquad
\newline
Area
A
=
b
h
A=b h
A
=
bh
0
0
0
\qquad
\newline
Copyright (c)
2006
2006
2006
Pearson Education Canada Inc.
\newline
Area
A
=
b
h
A=b h
A
=
bh
0
0
0
\qquad
Perimeter
A
=
b
h
A=b h
A
=
bh
0
0
0
\qquad
Area
A
=
b
h
A=b h
A
=
bh
0
0
0
\qquad
Get tutor help
MTH
1
1
1
W
1
1
1
\newline
SPIRAL
3
3
3
TAKE HOME ASSIGNMENT
\newline
Communication
\newline
6
6
6
. This is a LEVELLED CHOICE QUESTION. Answer at least one of the following qu
\newline
Create a fully simplified expression for the area of a square with a side length of
3
x
3 x
3
x
.
\newline
area of square
=
(
side length
)
2
or
(
side
)
(
side
)
\text { area of square }=(\text { side length })^{2} \quad \text { or } \quad(\text { side })(\text { side })
area of square
=
(
side length
)
2
or
(
side
)
(
side
)
Get tutor help
19
19
19
The area of a parallelogram
A
B
C
D
\mathrm{ABCD}
ABCD
is
192
s
q
.
c
m
192 \mathrm{sq.} \mathrm{cm}
192
sq.
cm
, and its height is
24
c
m
24 \mathrm{~cm}
24
cm
. Find the length of the base of parallelogram
A
B
C
D
A B C D
A
BC
D
. సమాంతర చతుర్పుజం ABCD యొక్క వైశాల్యం
192
192
192
చ.సెం.మీ. మరియు దాని ఎత్తు
24
24
24
సెం.మీ. అయినా ఆ సమాంతర చతుర్భుజం ABCD యొక్క భూమి పొడవు ను కనుగొనండి.
\newline
A
8
c
m
8 \mathrm{~cm}
8
cm
8
8
8
సెం.మీ.
\newline
B
16
c
m
16 \mathrm{~cm}
16
cm
\newline
16
16
16
సెం.మీ.
\newline
C
168
c
m
168 \mathrm{~cm}
168
cm
\newline
D
216
c
m
216 \mathrm{~cm}
216
cm
\newline
168
168
168
సెం.మీ.
\newline
216
216
216
సెం.మీ.
\newline
20
20
20
Express
16000
16000
16000
in standard form.
\newline
16000
16000
16000
ని ప్రామాణిక రూపంలో వ్యక్తపరచండి.
\newline
A
1.6
×
1
0
4
1.6 \times 10^{4}
1.6
×
1
0
4
\newline
[B]
1.6
×
1
0
3
1.6 \times 10^{3}
1.6
×
1
0
3
\newline
C
192
s
q
.
c
m
192 \mathrm{sq.} \mathrm{cm}
192
sq.
cm
0
0
0
\newline
7
7
7
/
12
12
12
\newline
Section B: Answer the following questions in your ansh.....ets. సెక్షన్ B: మీ జవాబు పత్రంలో ఈ క్రింది ప్రశ్నలకు సమాధానాలు ఇవ్వండి.
\newline
192
s
q
.
c
m
192 \mathrm{sq.} \mathrm{cm}
192
sq.
cm
1
1
1
\newline
21
21
21
a) A student scores
35
35
35
on the first quiz and
50
50
50
on the second quiz. Calculate the percentage increase in their marks. ఒక విద్యార్థికి మొదటి క్విజ్లో స్కోరు
35
35
35
, రెండవ క్విజ్లో స్కోర్
50
50
50
వచ్చిన యెడల, అతనికి వచ్చిన మార్కులలో పెరిగిన శాతమెంత?
\newline
b) A dress is sold at Rs.
92
92
92
with a profit of
192
s
q
.
c
m
192 \mathrm{sq.} \mathrm{cm}
192
sq.
cm
2
2
2
. What is the original cost price of the dress?
\newline
192
s
q
.
c
m
192 \mathrm{sq.} \mathrm{cm}
192
sq.
cm
2
2
2
లాభంతో ఒక డ్రెస్ ను రూ.
92
92
92
కు అమ్మిన, డ్రెస్ యొక్క అసలు ధరను కనుగొనుము.
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7
7
7
\newline
MR
\newline
19
19
19
The area of a parallelogram
A
B
C
D
\mathrm{ABCD}
ABCD
is
192
s
q
.
c
m
192 \mathrm{sq} . \mathrm{cm}
192
sq
.
cm
, and its height
24
c
m
24 \mathrm{~cm}
24
cm
. Find the length of the base of parallelogram
A
B
C
D
A B C D
A
BC
D
. సమాంతర చతుర్తుజం ABCD యొక్క వైశాల్యం
192
192
192
చ.సెం.మీ. మరియు దాశా ఎత్తు
24
24
24
సెం.మీ. అయినా ఆ సమాంతర చతుర్ృుజం ABCD యొక్క భూవి పొడవు ను కనుగొనండి.
\newline
A
8
c
m
8 \mathrm{~cm}
8
cm
\newline
B
16
c
m
16 \mathrm{~cm}
16
cm
\newline
8
8
8
సెం.మీ.
\newline
16
16
16
సెం.మీ.
\newline
C
168
c
m
168 \mathrm{~cm}
168
cm
\newline
D
216
c
m
216 \mathrm{~cm}
216
cm
\newline
168
168
168
సెం.మీ.
\newline
216
216
216
సెం.మీ.
\newline
20
20
20
Express
16000
16000
16000
in standard form.
\newline
16000
16000
16000
ని ప్రామాణిక రూపంలో వ్యక్తపరచండి.
\newline
A
1.6
×
1
0
4
1.6 \times 10^{4}
1.6
×
1
0
4
\newline
B
1.6
×
1
0
3
1.6 \times 10^{3}
1.6
×
1
0
3
\newline
192
s
q
.
c
m
192 \mathrm{sq} . \mathrm{cm}
192
sq
.
cm
0
0
0
\newline
7
7
7
/
12
12
12
\newline
Section B: Answer the following questions in your ansh.....ets. సెక్షన్ B: మీ జవాబు పత్రంలో ఈ క్రింది ప్రశ్నలకు సమాధానాలు ఇవ్వండి.
\newline
192
s
q
.
c
m
192 \mathrm{sq} . \mathrm{cm}
192
sq
.
cm
1
1
1
\newline
21
21
21
a) A student scores
35
35
35
on the first quiz and
50
50
50
on the second quiz. Calculate the percentage increase in their marks. ఒక విద్యార్ధికి మొదటి క్విజ్లో స్కోరు
35
35
35
, రెండవ క్విజ్లో స్కోర్
50
50
50
వచ్చిన యెడల, అతనికి వచ్చిన మార్కులలో పెరిగిన శాతమెంత?
\newline
b) A dress is sold at Rs.
92
92
92
with a profit of
192
s
q
.
c
m
192 \mathrm{sq} . \mathrm{cm}
192
sq
.
cm
2
2
2
. What is the original cost price of the dress?
\newline
192
s
q
.
c
m
192 \mathrm{sq} . \mathrm{cm}
192
sq
.
cm
2
2
2
లాభంతో ఒక డ్రెస్ ను రూ.
92
92
92
కు అమ్మిన, డ్రెస్ యొక్క అసలు ధరను కనుగొనుము.
\newline
[ Turn
0
0
0
Get tutor help
π
=
3.14.1
\pi=3.14 .1
π
=
3.14.1
\newline
(
10
10
10
. Find the area of the shaded region. (Take
π
=
3.14
\pi=3.14
π
=
3.14
.)
\newline
Ans:
\qquad
\newline
As
\newline
15
15
15
. Find the area of the shaded region. (Take
π
=
3.14
\pi=3.14
π
=
3.14
)
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12
12
12
\newline
The illustration shows two circles of radii
4
c
m
4 \mathrm{~cm}
4
cm
and
2
c
m
2 \mathrm{~cm}
2
cm
respectively. The distance between the two centres is
8
c
m
8 \mathrm{~cm}
8
cm
. Find the length of the common tangent
[
A
B
]
[\mathrm{AB}]
[
AB
]
.
\newline
5.29
5.29
5.29
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⇒
5
=
2
x
−
x
=
x
⇒
x
=
5
\Rightarrow 5=2 x-x=x \Rightarrow x=5
⇒
5
=
2
x
−
x
=
x
⇒
x
=
5
\newline
Hence, Shobo's present age
=
5
=5
=
5
years and Shobo's mother's present age
=
6
×
5
=
30
=6 \times 5=30
=
6
×
5
=
30
years
\newline
1
1
1
. A number is such that it is as much greater than
84
84
84
as it is less than
108
108
108
. Find it.
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Question
3
3
3
\newline
1
p
t
s
1 \mathrm{pts}
1
pts
\newline
You wish to test the following claim
(
H
a
)
\left(\mathrm{H}_{\mathrm{a}}\right)
(
H
a
)
at a significance level of
α
=
0.05
\alpha=0.05
α
=
0.05
.
\newline
H
o
:
p
=
0.42
H
a
:
p
>
0.42
\begin{array}{l} \mathrm{H}_{\mathrm{o}}: p=0.42 \\ \mathrm{H}_{\mathrm{a}}: p>0.42 \end{array}
H
o
:
p
=
0.42
H
a
:
p
>
0.42
\newline
You obtain a sample of size
n
=
143
n=143
n
=
143
in which there are
73
73
73
successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.
\newline
What is the test statistic? Round to
2
2
2
decimal places.
\newline
2
2
2
.
192
192
192
\newline
2
2
2
.
19
19
19
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The diagram shows a container consisting of a square open top with rectangular sides, each
10
x
c
m
10 x \mathrm{~cm}
10
x
cm
by
h
c
m
h \mathrm{~cm}
h
cm
, and an inverted regular pyramid. The perpendicular height of the pyramid is
10
r
c
m
12
x
c
m
10 \mathrm{r} \mathrm{cm} 12 x \mathrm{~cm}
10
r
cm
12
x
cm
.
\newline
(i) Find an expression in terms of
x
x
x
for the area of one triangular face of the pyramid.
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You wish to test the following claim
(
H
a
)
\left(H_{a}\right)
(
H
a
)
at a significance level of
α
=
0.10
\alpha=0.10
α
=
0.10
.
\newline
H
o
:
μ
=
60.8
H
a
:
μ
>
60.8
\begin{array}{l} H_{o}: \mu=60.8 \\ H_{a}: \mu>60.8 \end{array}
H
o
:
μ
=
60.8
H
a
:
μ
>
60.8
\newline
You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:
\newline
\begin{tabular}{|r|}
\newline
\hline data \\
\newline
\hline
64
64
64
.
8
8
8
\\
\newline
\hline
33
33
33
.
6
6
6
\\
\newline
\hline
69
69
69
.
6
6
6
\\
\newline
\hline
54
54
54
.
7
7
7
\\
\newline
\hline
79
79
79
\\
\newline
\hline
69
69
69
.
6
6
6
\\
\newline
\hline
86
86
86
.
9
9
9
\\
\newline
\hline
69
69
69
.
6
6
6
\\
\newline
\hline
93
93
93
.
5
5
5
\\
\newline
\hline
99
99
99
.
2
2
2
\\
\newline
\hline
90
90
90
.
6
6
6
\\
\newline
\hline
76
76
76
.
7
7
7
\\
\newline
\hline
65
65
65
.
8
8
8
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the critical value for this test? (Report answer accurate to three decimal places.)
\newline
critical value
=
1.356
=1.356
=
1.356
\newline
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
\newline
test statistic
=
=
=
□
\square
□
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8
8
8
: Circular Measure
\newline
In the diagram,
O
O
O
is the centre of the circle
A
C
B
Q
A C B Q
A
CBQ
of radius
20
c
m
.
A
P
B
20 \mathrm{~cm} . A P B
20
cm
.
A
PB
jom arc of a circle with centre
C
C
C
and angle
A
C
B
=
1.4
A C B=1.4
A
CB
=
1.4
radians.
C
P
C P
CP
bisects
∠
A
C
B
\angle A C B
∠
A
CB
.
\newline
(a) Find otuge angle
A
O
B
A O B
A
OB
in radians.
\newline
[
1
]
[1]
[
1
]
\newline
(b) Show that
A
C
=
30.59
A C=30.59
A
C
=
30.59
cm correct to
2
2
2
decimal places.
\newline
(c) Calculate the perimeter of the shaded region.
\newline
(d) Calculate the area of the shaded region.
\newline
[Ans: (a)
A
C
B
Q
A C B Q
A
CBQ
0
0
0
(b)
30
30
30
.
59
59
59
\newline
(c)
A
C
B
Q
A C B Q
A
CBQ
1
1
1
\newline
(d)
A
C
B
Q
A C B Q
A
CBQ
2
2
2
]
\newline
[
4
4
4
]
\newline
[
3
3
3
]
\newline
[
3
3
3
]
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Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points, to the nearest tenth (if necessary).
\newline
(
7
,
−
7
)
and
(
1
,
1
)
(7,-7) \text { and }(1,1)
(
7
,
−
7
)
and
(
1
,
1
)
\newline
*Click twice to draw a line. Click a segment to erase it.
∗
{ }^{*}
∗
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
Leg
1
1
1
:
□
\square
□
Leg
2
2
2
:
□
\square
□
Distance:
□
\square
□
\newline
Submit Answer
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7
7
7
A logo is designed with four identical squares. A triangle is drawn in each square as shown. Find the total area of the four triangles.
\newline
Area of figure
=
8
c
m
×
5
c
m
=
64
c
m
2
\begin{aligned} \text { Area of figure } & =8 \mathrm{~cm} \times 5 \mathrm{~cm} \\ & =64 \mathrm{~cm}^{2}\end{aligned}
Area of figure
=
8
cm
×
5
cm
=
64
cm
2
\newline
Ans:
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1
1
1
For a square of sides
x
c
m
x \mathrm{~cm}
x
cm
, write the formulae for its perimeter
P
P
P
and area
A
A
A
in terms of
x
x
x
.
Get tutor help
The scatter plot and line of best fit below show the length of
12
12
12
people's femur (the long leg bone in the thigh) and their height in centimeters. Based on the line of best fit, what would
b
b
b
the predicted height for someone with a femur length of
55
c
m
55 \mathrm{~cm}
55
cm
?
Get tutor help
A
(
x
)
=
(
8
+
2
x
)
2
A(x) = (8 + 2x)^2
A
(
x
)
=
(
8
+
2
x
)
2
\newline
Carmen wants to add a border around a square picture. The function shows the area of the picture in square inches if it has a border
x
x
x
inches wide. What are the dimensions of the picture without the border?
Get tutor help
Extend
\newline
14
14
14
. From the top of a
35
−
m
35-\mathrm{m}
35
−
m
-tall building, an observer sees a truck heading toward the building at an angle of depression of
1
0
∘
10^{\circ}
1
0
∘
. Ten seconds later, the angle of depression to the truck is
2
5
∘
25^{\circ}
2
5
∘
.
\newline
a) Determine the distance that the truck has travelled. Express your answer to the nearest metre.
\newline
b) If the speed limit for the area is
40
k
m
/
h
40 \mathrm{~km} / \mathrm{h}
40
km
/
h
, is the truck driver following the speed limit? Explain.
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QUESTION
1
1
1
\newline
Metals are bolated frem ther ores by reacting the metal exide with carbon as shown in the following equation.
\newline
Z
M
O
(
s
)
+
C
(
s
)
→
Z
M
(
s
)
+
C
O
2
(
g
)
\mathrm{ZMO}(\mathrm{s})+\mathrm{C}(\mathrm{s}) \rightarrow \mathrm{ZM}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})
ZMO
(
s
)
+
C
(
s
)
→
ZM
(
s
)
+
CO
2
(
g
)
\newline
II
18.6
g
18.6 \mathrm{~g}
18.6
g
of a pure metal oxibe reacted with excess cartion
4.98
L
4.98 \mathrm{~L}
4.98
L
of
C
O
2
\mathrm{CO}_{2}
CO
2
gas was formed at
20
0
∘
C
200^{\circ} \mathrm{C}
20
0
∘
C
and the pressure at
1.80
a
t
m
1.80 \mathrm{~atm}
1.80
atm
. What is the ibentity of metal,
M
\mathrm{M}
M
?
\newline
H
g
\mathrm{Hg}
Hg
\newline
N
g
9
\mathrm{Ng}_{9}
Ng
9
\newline
C
u
\mathrm{Cu}
Cu
\newline
C
a
\mathrm{Ca}
Ca
\newline
Un
\newline
4.98
L
4.98 \mathrm{~L}
4.98
L
0
0
0
\newline
4.98
L
4.98 \mathrm{~L}
4.98
L
0
0
0
\newline
QUESTION
2
2
2
\newline
4.98
L
4.98 \mathrm{~L}
4.98
L
2
2
2
\newline
4.98
L
4.98 \mathrm{~L}
4.98
L
3
3
3
\newline
4.98
L
4.98 \mathrm{~L}
4.98
L
4
4
4
Get tutor help
rimeter, Area, and Voly.me
\newline
ce area of a trizhgular prism
\newline
surface area of this triangular prism. Be sure to include the correct unit in your answer.
\newline
□
\square
□
\newline
□
\square
□
c
m
\mathrm{cm}
cm
\newline
xplanation
\newline
Check
Get tutor help
i-Ready
\newline
Nets and Surface Area - Quiz - Level F
\newline
A net for a three-dimensional figure is shown on grid paper. Each square of the grid paper represents
1
1
1
in.?.
\newline
What is the surface area of the three-dimensional figure?
\newline
S.A.
=
65
=65 \quad
=
65
in.
2
^{2}
2
\newline
\begin{tabular}{|c|c|c|c|}
\newline
\hline \multicolumn{
4
4
4
}{|c|}{
…
\ldots
…
} \\
\newline
\hline
7
7
7
&
8
8
8
&
9
9
9
&
x
\mathbf{x}
x
\\
\newline
\hline
4
4
4
&
5
5
5
&
6
6
6
& - \\
\newline
\hline
1
1
1
&
2
2
2
&
3
3
3
&
→
\rightarrow
→
\\
\newline
\hline
0
0
0
& . & & \\
\newline
\hline
\newline
\end{tabular}
\newline
DONE
Get tutor help
TRY IT YOURSELF
2
2
2
\newline
In the diagram,
O
O
O
is the centre of the circle, diameter
A
C
=
5
m
,
A
B
=
4
m
A C=5 \mathrm{~m}, A B=4 \mathrm{~m}
A
C
=
5
m
,
A
B
=
4
m
and
B
C
=
3
m
B C=3 \mathrm{~m}
BC
=
3
m
. Find
\newline
(a) the length of
B
D
B D
B
D
,
\newline
(b) the area of the shaded region,
\newline
(c) the perimeter of the shaded region.
\newline
Give your answers in terms of
π
\pi
π
if necessary.
Get tutor help
Water is poured into an inverted conical container which has height
12
c
m
12 \mathrm{~cm}
12
cm
and radius
8
c
m
8 \mathrm{~cm}
8
cm
. After some time, the depth of water in the container is
h
c
m
h \mathrm{~cm}
h
cm
and the area of water not in contact with the container is
A
c
m
2
A \mathrm{~cm}^{2}
A
cm
2
. Given that the rate of change of
A
A
A
is
0.6
c
m
2
s
−
1
0.6 \mathrm{~cm}^{2} \mathrm{~s}^{-1}
0.6
cm
2
s
−
1
when
r
=
4.8
c
m
r=4.8 \mathrm{~cm}
r
=
4.8
cm
, find
\newline
(i)
d
r
d
t
\quad \frac{\mathrm{d} r}{\mathrm{~d} t}
d
t
d
r
in terms of
π
\pi
π
,
\newline
(ii) the rate at which
V
V
V
is increasing at that instant.
Get tutor help
Question
\newline
A spherical balloon is being filled with air at the constant rate of
4
c
m
3
/
s
e
c
4 \mathrm{~cm}^{3} / \mathrm{sec}
4
cm
3
/
sec
. How fast is the radius increasing when the radius is
7
c
m
7 \mathrm{~cm}
7
cm
?
\newline
Submit an exact answer in terms of
π
\pi
π
.
Get tutor help
Val needs to find the area enclosed by the figure. The figure i. made by attaching semicircles to each side of a
46
−
m
−
b
y
−
46
−
m
46-m-b y-46-m
46
−
m
−
b
y
−
46
−
m
square. Val says the area is
1
,
206.12
m
2
1,206.12 m^{2}
1
,
206.12
m
2
. Fididine area enclosed by the figure. Use
3
3
3
.
14
14
14
for
π
\pi
π
. What error might
V
V
V
al have made?
\newline
Question Help
\newline
The area enclosed by the figure is
□
\square
□
m
2
\mathrm{m}^{2}
m
2
\newline
(Round to the nearest hundredth as needed.)
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Calculate the area of the rectangle when
a
=
4
a=4
a
=
4
and
b
=
2
b=2
b
=
2
. Next, calculate the area when the length and width are doubled. Does the area double? What is the ratio of the two areas you calculated?
\newline
(A) NO;
1
:
4
1:4
1
:
4
\newline
(B) YES;
1
:
4
1:4
1
:
4
\newline
(C) NO;
1
:
2
1:2
1
:
2
\newline
(D) YES;
1
:
2
1:2
1
:
2
Get tutor help
- perimeter of the shaded region
=
(
25
π
+
56
)
c
m
=(25 \pi+56) \mathrm{cm}
=
(
25
π
+
56
)
cm
\newline
TRY IT
\newline
YOURSELF
2
2
2
\newline
In the diagram,
O
O
O
is the centre of the circle, diameter
A
C
=
5
m
,
A
B
=
4
m
A C=5 \mathrm{~m}, A B=4 \mathrm{~m}
A
C
=
5
m
,
A
B
=
4
m
and
B
C
=
3
m
B C=3 \mathrm{~m}
BC
=
3
m
. Find
\newline
(a) the length of
B
D
B D
B
D
,
\newline
(b) the area of the shaded region,
\newline
(c) the perimeter of the shaded region.
\newline
Give your answers in terms of
π
\pi
π
if necessary.
Get tutor help
8
8
8
. Mrs. Thayer and Mr. Darst are each driving a car. Mr. Darst's wheel has a diameter of
15
15
15
inches, and Mrs. Thayer's wheel has a diameter of
18
18
18
inches. If their wheels rotate
8
8
8
revolutions, how many inches further does Mrs. Thayer's travel, rounded to the nearest tenth?
\newline
Darst
\newline
d
=
15
d=15
d
=
15
ver
=
8
=8
=
8
\newline
c
=
π
=
7.5
c=\pi=7.5
c
=
π
=
7.5
\newline
Find
m
∠
F
G
H
m \angle F G H
m
∠
FG
H
in
⊙
G
\odot G
⊙
G
, rounded
\newline
to the nearest degree.
\newline
Thayer
\newline
d
=
18
d=18
d
=
18
rev
=
8
=8
=
8
\newline
r
=
9
r=9
r
=
9
\newline
c
=
π
d
c=\pi d
c
=
π
d
=
18
π
=18 \pi
=
18
π
=
8
=8
=
8
0
0
0
10
10
10
. Find
=
8
=8
=
8
1
1
1
in
=
8
=8
=
8
2
2
2
, rounded
=
8
=8
=
8
3
3
3
to the nearest degree.
\newline
80
part
64
π
whole
=
x
yart
80
⋅
360
whole
E
28800
64
π
=
64
π
x
64
π
1430
=
x
\begin{array}{l} \frac{80 \text { part }}{64 \pi \text { whole }}=x \text { yart } \\ 80 \cdot 360 \text { whole } \\ \mathrm{E} \frac{28800}{64 \pi}=\frac{64 \pi x}{64 \pi} \\ 1430=x \end{array}
64
π
whole
80
part
=
x
yart
80
⋅
360
whole
E
64
π
28800
=
64
π
64
π
x
1430
=
x
\newline
=
8
=8
=
8
4
4
4
\newline
11
11
11
. Find the
=
8
=8
=
8
5
5
5
and the area of
=
8
=8
=
8
6
6
6
. Round to the nearest hundredth.
\newline
m
∠
L
O
Q
=
m \angle L O Q=
m
∠
L
OQ
=
\newline
area of
=
8
=8
=
8
7
7
7
=
8
=8
=
8
0
0
0
\newline
12
12
12
. Find the radius of the circle, given the area of the sector is
157
157
157
.
5
5
5
square
=
8
=8
=
8
9
9
9
. Round to the nearest centimeter.
\newline
r
=
r=
r
=
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The expression
s
2
s^{2}
s
2
is used to calculate the areag of a square, where
s
s
s
is the side length of the square. What does the expression
(
8
x
)
2
(8 x)^{2}
(
8
x
)
2
represent?
\newline
(A) the area of a square with a side length of
8
8
8
\newline
(B) the area of a square with a side length of
16
16
16
\newline
(C) the area of a square with a side length of
4
x
4 x
4
x
\newline
(D) the area of a square with a side length of
8
x
8 x
8
x
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The figure is made up of a rectangle, four identical quarter circles and two identical semicircles. Find its perimeter and area. (Take
π
=
22
7
\pi=\frac{22}{7}
π
=
7
22
.)
\newline
Area of
D
=
1
x
14
×
π
r
2
=
1
4
×
22
7
×
28
×
28
=
616
m
2
Area of
4
A
=
616
×
4
=
2464
m
2
\begin{array}{l} \text { Area of } D=\frac{1}{x_{14}} \times \pi r^{2} \\ =\frac{1}{4} \times \frac{22}{7} \times 28 \times 28 \\ =616 \mathrm{~m}^{2} \\ \text { Area of } 4 A=616 \times 4 \\ =2464 \mathrm{~m}^{2} \\ \end{array}
Area of
D
=
x
14
1
×
π
r
2
=
4
1
×
7
22
×
28
×
28
=
616
m
2
Area of
4
A
=
616
×
4
=
2464
m
2
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(
5
5
5
) A rectangular tank of height
40
c
m
40 \mathrm{~cm}
40
cm
had a base area of
300
c
m
2
300 \mathrm{~cm}^{2}
300
cm
2
. It was filled with water to a depth of
30
c
m
30 \mathrm{~cm}
30
cm
. After some water was poured out, the depth of the water decreased to
20
c
m
20 \mathrm{~cm}
20
cm
. How much water was poured out? Give your answer in litres. (
ℓ
=
1000
c
m
3
\ell=1000 \mathrm{~cm}^{3}
ℓ
=
1000
cm
3
)
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AREA \& PERIMETER PRACTICE
\newline
Find the area of each shape by counting square units.
\newline
1
1
1
\newline
\begin{tabular}{|l|l|l|l|}
\newline
\hline & & & \\
\newline
\hline & & & \\
\newline
\hline & & & \\
\newline
\hline & & & \\
\newline
\hline
\newline
\end{tabular}
\newline
2
2
2
\newline
\begin{tabular}{|l|l|l|l|l|}
\newline
\hline & & & & \\
\newline
\hline & & & & \\
\newline
\hline
\newline
\end{tabular}
\newline
Area: square units
\newline
Area: square units
\newline
Use the correct formula to find the area of each shape.
\newline
Area:
\newline
Area:
\newline
3
3
3
8
c
m
8 \mathrm{~cm}
8
cm
.
\newline
2
c
m
2 \mathrm{~cm}
2
cm
.
\newline
4
4
4
5
5
5
in.
5
5
5
in.
\newline
Area:
\newline
Area:
\newline
Page
1
1
1
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Find the area of a rhombus if its vertices are
(
3
,
0
)
,
(
4
,
5
)
,
(
−
1
,
4
)
(3,0),(4,5),(-1,4)
(
3
,
0
)
,
(
4
,
5
)
,
(
−
1
,
4
)
and
(
−
2
,
−
1
)
(-2,-1)
(
−
2
,
−
1
)
taken in order. [Hint : Area of a rhombus
=
1
2
=\frac{1}{2}
=
2
1
(product of its diagonals)]
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EUREKA MATH
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Next
\newline
Calculating Consumer Discounts: Mastery Test
\newline
Select the correct answer:
\newline
savings
=
=
=
price
×
\times
×
discount percentage
\newline
How much will you save if you buy an item listed at
$
75.50
\$ 75.50
$75.50
\newline
A.
$
18.88
\$ 18.88
$18.88
\newline
B.
$
25.00
\$ 25.00
$25.00
\newline
C.
$
56.62
\$ 56.62
$56.62
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A gemcutter wants to trim a gemstone that is approximately a regular octahedron with sides measured in millimeters (mm). She will remove imperfections by reducing the length of each side by
x
x
x
mm. The approximate new surface area is given in
mm
2
\text{mm}^2
mm
2
by the function:
\newline
S
(
x
)
=
3.4
(
56.25
−
15
x
+
x
2
)
S(x)=3.4(56.25-15x+x^2)
S
(
x
)
=
3.4
(
56.25
−
15
x
+
x
2
)
\newline
What is the current length of each side?
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8
8
8
−
30
-30
−
30
. Remember that a square is a rectangle with four equal sides.
\newline
a. If a square has an area of
81
81
81
square units, how long is each side?
\newline
b. Find the length of the side of a square with area
225
225
225
square units.
\newline
c. Find the length of the side of a square with area
10
10
10
square units.
\newline
d. Find the area of a square with side
11
11
11
units.
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rental membership is
$
231
\$ 231
$231
. A registration fee of
$
15
\$ 15
$15
is
F
\mathrm{F}
F
and the rest is paid monthly. How much do new membe month?
\newline
Attend to Precision Beverly is making peanut bu Janana bread. She always doubles the amount of nuts eanut butter chips. The total amount of chips and nut loubling is
4
1
2
4 \frac{1}{2}
4
2
1
cups. Write and solve an equation to fin riginal amount of nuts in the recipe.
\newline
oblems
4
4
4
−
7
-7
−
7
, solve each equation. Check your solutio
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A gardener will use up to
250
250
250
square feet for planting flowers and vegetables. She wants the area used for vegetables to be at least four times the area used for flowers. Let
x
x
x
denote the area (In square feet) used for flowers. Let
y
y
y
denote the area (In square feet) used for vegetables. Shade the reglon corresponding to all values of
x
x
x
and
y
y
y
that satisfy these requirements.
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The rectangular floor of a classroom is
38
38
38
feet in length and
32
32
32
feet in width. A scale drawing of the floor has a length of
19
19
19
inches. What is the area, in square inches, of the floor in the scale drawing?
\newline
Answer:
□
\square
□
in.
2
^{2}
2
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The rectangular floor of a classroom is
20
20
20
feet in length and
32
32
32
feet in width. A scale drawing of the floor has a length of
5
5
5
inches. What is the area, in square inches, of the floor in the scale drawing?
\newline
Answer:
□
\square
□
in.
2
^{2}
2
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The rectangular floor of a classroom is
40
40
40
feet in length and
20
20
20
feet in width. A scale drawing of the floor has a length of
20
20
20
inches. What is the area, in square inches, of the floor in the scale drawing?
\newline
Answer:
□
\square
□
in.
2
^{2}
2
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A piece of wire of length
57
57
57
is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square? Question content area bottom Part
1
1
1
(a) To minimize the combined area, the wire should be cut so that enter your response here are used for the circle and enter your response here are used for the square
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