Answer:
228.36 ft^2
Step-by-step explanation:
1. The total surface area is the area of two trapezoids and 4 rectangles. The rectangles all have the same width, so we can figure their area by finding their total length: the perimeter of the trapezoid.
rectangle area
The perimeter of the isosceles trapezoid is the sum of its edge lengths:
P = 13 +8.06 +5 +8.06 = 34.12
The rectangles are 3 ft wide, so their total area is ...
A = LW = (34.12 ft)(3 ft) = 102.36 ft^2
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trapezoid area
The area of a trapezoid is given by the formula ...
A = (1/2)(b1 +b2)h
A = (1/2)(13 ft +5 ft)(7 ft) = 63 ft^2
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total area
As we said, the total area is the sum of the rectangle area and that of two trapezoids:
total area = rectangle area + 2 × trapezoid area
A = 102.36 ft^2 + 2 × 63 ft^2
A = 228.36 ft^2
The area of the trapezoidal prism in figure 1 is 228.36 square feet.
