Question

Given a coordinate plane with the vertices of a polygon as follows: A(-4, 2), B(3, 2), C(3, -5), and D(-4, -2). What is the area of polygon ABCD?

A) 28 units squared
B) 38.5 units squared
C) 40.5 units squared
D) 49 units squared

Answer 1

The area of polygon ABCD is calculated by determining the shape is a rectangle, then multiplying the width (7 units) by the height (7 units) to get 49 units squared.

Step-by-step explanation:

To find the area of polygon ABCD with vertices A(-4, 2), B(3, 2), C(3, -5), and D(-4, -2), we must first identify the shape of the polygon. The coordinates suggest that we are dealing with a rectangle, as opposite sides are parallel and of equal length. The width of the rectangle can be found by subtracting the x-coordinate of A from the x-coordinate of B, resulting in a width of |3 - (-4)| = 7 units. Similarly, the height can be calculated by substracting the y-coordinate of C from the y-coordinate of B, which gives |2 - (-5)| = 7 units. Multiplying the width and height together gives us the area of the rectangle:

Area = width × height = 7 units × 7 units = 49 units squared.

Therefore, the correct answer is D) 49 units squared.