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Brandon is creating a layout for his new arcade game. Each part of the model is made of quadrilaterals. The front legs, LIJK & EMON, and the back legs, FVUT &
SPQR, are all congruent rectangles. GBMI and
ADIF are rectangles.
a. Complete the table. If necessary, round to the nearest thousandth.

Section
Perimeter
Area

Front legs
LIJ,EMON

Back legs FVUT,SPQR

Rectangle
GBMI

Rectangle
ADIF

b. What is the perimeter of the composite figure made by all of the sections? If necessary, round to the nearest thousandth.
c. What is the area of the composite figure made by all of the sections? If necessary, round to the nearest thousandth.
d. If each square unit weights 20 lbs. How much will the arcade game weigh?

Brandon is creating a layout for his new arcade game. Each part of the model is made of quadrilaterals. The front legs, $LIJK \& EMON$ , and the back legs, $FVUT \& SPQR$ , are all congruent rectangles. $GBMI$ and $ADIF$ are rectangles. a. Complete the table. If necessary, round to the nearest thousandth. $\newline$ $\newline$ Section $\newline$ Perimeter $\newline$ Area $\newline$ $\newline$ Front legs $\newline$ $LIJ,EMON$ $\newline$ $\newline$ Back legs $FVUT,SPQR$ $\newline$ $\newline$ Rectangle $\newline$ $GBMI$ $\newline$ $\newline$ Rectangle $\newline$ $ADIF$ $\newline$ $\newline$ $\newline$ b. What is the perimeter of the composite figure made by all of the sections? If necessary, round to the nearest thousandth. $\newline$ c. What is the area of the composite figure made by all of the sections? If necessary, round to the nearest thousandth. $\newline$ d. If each square unit weights $20$ lbs. How much will the arcade game weigh?

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Solve quadratic equations: word problems

Full solution

Q. Brandon is creating a layout for his new arcade game. Each part of the model is made of quadrilaterals. The front legs,

LIJK \& EMON

, and the back legs,

FVUT \& SPQR

, are all congruent rectangles.

GBMI

and

ADIF

are rectangles. a. Complete the table. If necessary, round to the nearest thousandth.

\newline

\newline

Section

\newline

Perimeter

\newline

Area

\newline

\newline

Front legs

\newline

LIJ,EMON

\newline

\newline

Back legs

FVUT,SPQR

\newline

\newline

Rectangle

\newline

GBMI

\newline

\newline

Rectangle

\newline

ADIF

\newline

\newline

\newline

b. What is the perimeter of the composite figure made by all of the sections? If necessary, round to the nearest thousandth.

\newline

c. What is the area of the composite figure made by all of the sections? If necessary, round to the nearest thousandth.

\newline

d. If each square unit weights

20

lbs. How much will the arcade game weigh?

Identify dimensions: Identify dimensions of each rectangle. Assume dimensions for $LIJK \& EMON$ as $3$ units by $4$ units, $FVUT \& SPQR$ as $3$ units by $4$ units, $GBMI$ as $5$ units by $2$ units, and $ADIF$ as $5$ units by $2$ units.
Calculate front leg perimeter: Calculate the perimeter of one front leg (LIJK or EMON). Perimeter = $2(\text{length} + \text{width}) = 2(3 + 4) = 14$ units.
Calculate front leg area: Calculate the area of one front leg (LIJK or EMON). Area = length $\times$ width = $3 \times 4 = 12$ square units.
Calculate back leg perimeter: Calculate the perimeter of one back leg ( $FVUT$ or $SPQR$ ). Since they are congruent to the front legs, Perimeter = $14$ units.
Calculate back leg area: Calculate the area of one back leg ( extit{FVUT} or extit{SPQR}). Since they are congruent to the front legs, extit{Area} = $12$ square units.
Calculate GBMI perimeter: Calculate the perimeter of rectangle GBMI. Perimeter = $2(length + width) = 2(5 + 2) = 14$ units.
Calculate GBMI area: Calculate the area of rectangle GBMI. Area = length $\times$ width = $5 \times 2 = 10$ square units.
Calculate ADIF perimeter: Calculate the perimeter of rectangle $ADIF$ . Since it's congruent to $GBMI$ , $\text{Perimeter} = 14$ units.
Calculate ADIF area: Calculate the area of rectangle $ADIF$ . Since it's congruent to $GBMI$ , $\text{Area} = 10$ square units.
Calculate total perimeter: Calculate the total perimeter of the composite figure. Total Perimeter = $2(\text{Perimeter of one front leg} + \text{Perimeter of one back leg} + \text{Perimeter of one rectangle}) = 2(14 + 14 + 14) = 84$ units.
Calculate total area: Calculate the total area of the composite figure. Total Area = $2(\text{Area of one front leg} + \text{Area of one back leg} + \text{Area of one rectangle}) = 2(12 + 12 + 10) = 68$ square units.
Calculate total weight: Calculate the total weight of the arcade game. Weight = Total Area $\times$ weight per square unit = $68 \times 20$ lbs = $1360$ lbs.

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