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1152 ft^2

Step-by-step explanation:

There are 7 faces on this solid.

I will label the faces and will calculate each area with an explanation.

Faces 1 and 2:

The front face and the back face are congruent and have 5 sides each. Each face is a rectangle with a triangle above it. The lower rectangular part has dimensions 9 ft by 12 ft. The triangle above the rectangle has base 9 ft and height 16 ft - 12 ft = 4 ft.

Each face is a rectangle and a triangle.

area = area of rectangle + area of triangle

area = LW + bh/2

area = 9 ft * 12 ft + 9 ft * 4 ft/2 = 108 ft^2 + 18 ft^2 = 126 ft^2

This is area of of face 1, the front face. Face 2, the rear face has the same area.

A1 = 126 ft^2

A2 = 126 ft^2

Face 3: The bottom of the solid is a rectangle measuring 9 ft by 20 ft

area = LW

area = 9 ft * 20 ft = 180 ft^2

A3 = 180 ft^2

Faces 4 and 5:

The left vertical face and the right vertical face are congruent rectangles measuring 12 ft by 20 ft.

area = LW

area = 12 ft * 20 ft = 240 ft^2

A4 = 240 ft^2

A5 = 240 ft^2

Faces 6 and 7 are the top right and left inclined rectangles. They are congruent, and each one has dimensions 6 ft by 20 ft.

area = LW

area = 6 ft * 20 ft = 120 ft^2

We need 2 of these area.

A6 = 120 ft^2

A7 = 120 ft^2

total surface area = A1 + A2 + A3 + A4 + A5 + A6 + A7

total surface area = 126 ft^2 + 126 ft^2 + 180 ft^2 + 240 ft^2 + 240 ft^2 +  120 ft^2 + 120 ft^2

total surface area = 1152 ft^2

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step-by-step explanation: