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Geometry
Coordinate Perimeter & Area
Find the area and perimeter of the
Name
qquad

qquad Date
qquad

qquad Section
qquad

{:[D(-4","6)],[E(4","3)],[F(-4","0)]:}
E
(4,3)
Perimeter
=
qquad
Area
=
qquad

Geometry $\newline$ Coordinate Perimeter \& Area $\newline$ Find the area and perimeter of the $\newline$ Name $\qquad$ $\newline$ $\qquad$ Date $\qquad$ $\newline$ $\qquad$ Section $\qquad$ $\newline$ $\begin{array}{l} D(-4,6) \\ E(4,3) \\ F(-4,0) \end{array}$ $\newline$ E $(4,3)$ $\newline$ Perimeter $=$ $\qquad$ $\newline$ Area $=$ $\qquad$

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Area of quadrilaterals and triangles: word problems

Full solution

Q. Geometry

\newline

Coordinate Perimeter \& Area

\newline

Find the area and perimeter of the

\newline

Name

\qquad

\newline

\qquad

Date

\qquad

\newline

\qquad

Section

\qquad

\newline

\begin{array}{l} D(-4,6) \\ E(4,3) \\ F(-4,0) \end{array}

\newline

E

(4,3)

\newline

Perimeter

=

\qquad

\newline

Area

=

\qquad

Calculate DE distance: To find the perimeter, we need to calculate the distance between each pair of points. Let's start with the distance between D and E. $\newline$ Use the distance formula: $d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}$ . $\newline$ So, $DE = \sqrt{((4 - (-4))^2 + (3 - 6)^2)} = \sqrt{(8^2 + (-3)^2)} = \sqrt{64 + 9} = \sqrt{73}$ .
Calculate EF distance: Next, find the distance between E and F. $\newline$ $EF = \sqrt{((4 - (-4))^2 + (3 - 0)^2)} = \sqrt{(8^2 + 3^2)} = \sqrt{64 + 9} = \sqrt{73}$ .
Calculate FD distance: Now, find the distance between F and D. $FD = \sqrt{((-4 - (-4))^2 + (0 - 6)^2)} = \sqrt{(0)^2 + (-6)^2} = \sqrt{0 + 36} = \sqrt{36} = 6$ .
Calculate perimeter: Add up the distances to get the perimeter. $\newline$ Perimeter = $DE + EF + FD = \sqrt{73} + \sqrt{73} + 6$ .
Calculate semi-perimeter: To find the area, use Heron's formula: $A = \sqrt{s(s - a)(s - b)(s - c)}$ , where $s$ is the semi-perimeter. $\newline$ First, calculate the semi-perimeter: $s = (DE + EF + FD) / 2 = (\sqrt{73} + \sqrt{73} + 6) / 2$ .
Use Heron's formula: Now, plug the values into Heron's formula. $\newline$ $s = (\sqrt{73} + \sqrt{73} + 6) / 2 = (2\sqrt{73} + 6) / 2 = \sqrt{73} + 3$ . $\newline$ Area = $\sqrt{s(s - DE)(s - EF)(s - FD)} = \sqrt{(\sqrt{73} + 3)((\sqrt{73} + 3) - \sqrt{73})((\sqrt{73} + 3) - \sqrt{73})((\sqrt{73} + 3) - 6)}$ .
Simplify area expression: Simplify the expression for the area. $\newline$ Area = $\sqrt{(\sqrt{73} + 3)(3)(3)(-3)} = \sqrt{(\sqrt{73} + 3)(-27)}$ .

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