Answer:
80 square units
Explanation:
There are several ways to find the area of this figure.
a. trapezoid less triangle
If we draw a vertical line at x=4, it will complete the bounding outline of the figure, creating a trapezoid. The left-side "base" is 4-(-8) = 12 units long, and the right-side "base" is 4 -2 = 2 units long. The "height" is the difference in x-coordinates of the vertical bases, so is 4 -(-8) = 12 units.
The area of the trapezoid is then ...
A = 1/2(b1 +b2)h
A = 1/2(12 +2)(12) = 84 . . . square units
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The actual figure has a smaller area by the amount of the triangle cut from the upper right. That triangle has a base of 4-0 = 4 units, and a height of 4-2 = 2 units. Its area is ...
A = 1/2bh
A = 1/2(4)(2) = 4 . . . square units
Then the figure area of interest is the difference of the trapezoid area and the cut-out triangle area:
A = 84 -4 = 80 . . . square units.
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b. trapezoid plus triangle
If the short horizontal line is extended across the figure, it divides the figure into a trapezoid above the line and a triangle below the line. The upper trapezoid is 2 units high, and has bases 8 and 12. Its area is ...
A = 1/2(b1 +b2)h = 1/2(8 +12)(2) = 20 . . . square units
The triangle has a (horizontal) base of 12 units and a height of 10 units. Its area is ...
A = 1/2bh = 1/2(12)(10) = 60 . . . square units
The area of the figure is the sum of these areas:
A = 20 +60 = 80 . . . square units