Question

Below is a rectangle. What is the area? Units are in miles. Round to the nearest mile.

A is ( -4, 1) B is (-2, 4) C is (4,0) D is (2, -3)

Responses
a) 29mi^2
b) 18mi^2
c) 26mi^2
d) 32mi^2

Answer 1

To find the area of the rectangle, we need to find the length and the width.

First, we can find the lengths of the sides using the distance formula:
AB = √((-2 - (-4))^2 + (4 - 1)^2) = √(2^2 + 3^2) = √(4 + 9) = √13 ≈ 3.6 miles
CD = √((4 - 2)^2 + (0 - (-3))^2) = √(2^2 + 3^2) = √(4 + 9) = √13 ≈ 3.6 miles

Then, we can find the width of the rectangle using the distance formula:
BC = √((4 - (-2))^2 + (0 - 4)^2) = √(6^2 + 4^2) = √(36 + 16) = √52 ≈ 7.2 miles
AD = √((-4 - 2)^2 + (1 - (-3))^2) = √((-6)^2 + 4^2) = √(36 + 16) = √52 ≈ 7.2 miles

Since the opposite sides of a rectangle are equal in length, we can label AB = CD = 3.6 miles (length) and BC = AD = 7.2 miles (width).

Now, we can calculate the area of the rectangle:
Area = length * width
Area = 3.6 miles * 7.2 miles
Area = 25.92 ≈ 26 mi^2

Therefore, the area of the rectangle is approximately 26 mi^2.

c) 26mi^2