What is the area of this figure?

units^2

Total Area = 42

Step-by-step explanation:

|x| means the positive value of x. So |-5| = 5

Top Triangle

H: The height is the maximum y value from 4 to 2 or (4 - 2) which is 2. The x value for both points is the same (-1) and so the distance is unaffected by the x value.

B: The base line is the x value from -5 to 2. That is a little trickier. You can say it is |-5| + 2 = 7

Area: The formula for the area is 1/2 B * H

Area = 1/2 7*2 = 7 units^2

Rectangle

L = B: The Length of the rectangle = the base of the triangle (7 units.

W: The y value from 2 to |-2| or 2 + 2 = 4

Area: the formula for the area is A = L*W

Area = L*W

Area = 7 *4 = 28 units^2

Bottom Triangle

B: The base of this triangle = B of the top triangle. The numbers are exactly the same.

H: |-4| - | - 2 |

H: 4 - 2

H: 2

Area: The area = 1/2 * 2 * 7 = 7 square units.

Total Area

Total Area = 7 + 28 + 7 = 42