Question

Figure ABCD has vertices A(−2, 3), B(4, 3), C(4, −2), and D(−2, 0). What is the area of figure ABCD?

A) 6 square units
B) 12 square units
C) 18 square units
D) 24 square units

Answer 1

To find the area of figure ABCD, we can use the formula for the area of a rectangle. Since ABCD is a rectangle, we can calculate the length and width of the rectangle using the coordinates of its vertices.

The length of the rectangle is the distance between points A and B, which can be calculated using the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

d = sqrt((4 - (-2))^2 + (3 - 3)^2)

= sqrt(6^2 + 0^2)

= sqrt(36)

= 6

The width of the rectangle is the distance between points B and C, which can also be calculated using the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

d = sqrt((4 - 4)^2 + (-2 - 3)^2)

= sqrt(0^2 + (-5)^2)

= sqrt(25)

= 5

Now, we can use the formula for the area of a rectangle:

Area = length * width

= 6 * 5

= 30

Therefore, the area of figure ABCD is 30 square units.