Answer:
731 square feet
Step-by-step explanation:
The surface area can be found using the given formula, along with the formula for the area of a trapezoid. (The bases have the shape of a trapezoid.)
We are given "h", so we need to find "p" and "B" for the formula.
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Lateral Area dimensions
The perimeter is the sum of the side lengths:
p = 13 ft + 7 ft + 10 ft + 8 ft = 38 ft . . . perimeter
The height is shown as 15 ft.
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Base Area
The base area is the area of a trapezoid with base lengths 13 ft and 10 ft and height 7 ft. (The height is the perpendicular distance between the parallel bases. The two right angle corners show you the bases are parallel, and that 7 ft is the distance between them.)
A = 1/2(b1 +b2)h
A = 1/2(13 ft +10 ft)(7 ft) = 80.5 ft²
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Total Surface Area
Using your formula for the surface area, we find ...
SA = hp +2(B)
SA = (15 ft)(38 ft) +2(80.5 ft²) = 570 ft² +161 ft²
SA = 731 ft²
The area of the trapezoidal prism is 731 square feet.
