A storage shed has a roof that is a square-based pyramid. The sides of the shed are 37 m wide. The slant height of the pyramid is 35 m.
How many 1.8 m² shingles are needed to cover the lateral surfaces of the roof?
a. 1440 b. 1438
c. 1439
d. 1443
The lateral surface area of a square-based pyramid is given by the formula:
Lateral surface area = (Base perimeter / 2) * Slant height
In this case, the base perimeter is given by the sides of the shed (37 m), so the base perimeter is 37 * 4 = 148 m.
Therefore, the lateral surface area is (148 / 2) * 35 = 2590 m².
To determine how many 1.8 m² shingles are needed, divide the lateral surface area by the area of each shingle:
Number of shingles = Lateral surface area / Area of each shingle
Number of shingles = 2590 / 1.8 = 1438.889...
Rounding to the nearest whole number, the answer is 1439.
Therefore, the correct answer is c. 1439.