Question

What is the area, in square feet, of the shaded region?

What is the area, in square feet, of the nonshaded region?

Answer 1

Draw a line going from the intersection of the 2 foot line going up and the 2 foot line going across. Draw this line so it is parallel to the 16 foot line at the bottom.

The orange figure is now cut into 2 pieces. The bottom piece is a rectangle and the top piece is a trapezoid.

Trapezoid
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The area of a trapezoid = (a + b)*h/2; a and b are the parallel lines. h = 2 + 8 = 10 feet
a = 1
b = 8 - 2 -2 = 4 feet. You are going to have to draw the diagram carefully to get this answer.
a is on the right side of the trapezoid. b is on the left side.
h = 8 + 2 = 10 feet

Area = (1 +4)*10/2 =25 square feet.

Rectangle
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L= 8 feet
w = 2 feet
A = L * w
Area= 2 *8 = 16 square feet.

Total Area Orange
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Area = 16 + 25 = 41 square feet

Area of the Black Area
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Area = L*W - 41 Square feet
Area =16 *8 - 41 = 87 square feet