Question

Polygon ABCD has vertices A(0, 2), B(0, 8), C(7, 8), and D(7, 2). What is polygon ABCD and its perimeter? (Hint: Draw the polygon on the coordinate plane and find the slopes of each side.)

Answer 1

Below are the choices that can be found elsewhere:

A. rectangle; P = 26 linear units
B. square; P = 42 units2
C. parallelogram; P = 42 linear units
D. trapezoid; P = 26 linear units

The answer is A which is rectangle; P = 26 linear units

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Answer 2

Answer:

Perimeter = 26 units

Step-by-step explanation:

Polygon ABCD has vertices A(0, 2), B(0, 8), C(7, 8), and D(7, 2).

We need to find the perimeter of ABCD polygon.

Using distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$AB=\sqrt{(0-0)^2+(8-2)^2}=\sqrt{36}=6$

$BC=\sqrt{(7-0)^2+(8-8)^2}=\sqrt{49}=7$

$CD=\sqrt{(7-7)^2+(2-8)^2}=\sqrt{36}=6$

$DA=\sqrt{(7-0)^2+(2-2)^2}=\sqrt{49}=7$

Polygon is a rectangle because opposite sides are equal.

Perimeter of the polygon = AB + BC + CD + DA

                                          = 6 +7 + 6 + 7

                                          = 26

Hence, The perimeter of polygon is 26 units.