Question

(05.05)Polygon ABCD has the following vertices:

A(−3, 3), B(5, 5), C(5, −4), and D(−3, −4)

Calculate the area of the polygon.

A. 52 units squared
B.56 units squared
C. 64 units squared
D.72 units squared

Answer 1

Answer:

C. 64 unit squared

Step-by-step explanation:

We are given a polygon ABCD having co-ordinates A(−3, 3), B(5, 5), C(5, −4), and D(−3, −4).

As, we know that,

Area of a polygon = $|\frac{(x_{1}y_{2}-y_{1}x_{2})+(x_{2}y_{3}-y_{2}x_{3})+(x_{3}y_{4}-y_{3}x_{4})+(x_{4}y_{1}-y_{4}x_{1})}{2}|$

So, after substituting the values of the co-ordinates, we have,

Area of the polygon = $|\frac{(-3\times 5-3\times 5)+(5\times -4-5\times 5)+(5\times (-4)-(-4)\times (-3))+(-3\times 3-(-4)\times (-3))}{2}|$

i.e. Area of the polygon = $|\frac{(-15-15)+(-20-25)+(-20-12)+(-9-12)}{2}|$

i.e. Area of the polygon = $|\frac{-30-45-32-21}{2}|$

i.e. Area of the polygon = $|\frac{-128}{2}|$

i.e. Area of the polygon = |-64| unit squared.

i.e. Area of the polygon = 64 unit squared.

Hence, area of the given polygon is 64 unit squared.

Answer 2

Answer:

C. 64 units squared