Name: Michelle

Who is asking: Student
Level: Middle

Question: Mr. Moser is planning to replace the roof of his home. He needs to order a pack of shingles. Each pack covers 100 sq. ft. of roof. Without a ladder, Mr. Moser can not climb to the roof to measure it. Instead, he measures his attic and finds it to be 40 ft. long, 24 ft. wide, and 5 ft. high at the peak of the roof which is in the center of the house. Although the roof is even with the side walls, he estimates the roof line continues 1.5 ft. beyond the front and back walls. How many full packs of shingles should Mr. Moser order to cover his roof?

Hi Michelle,

I am not sure whether the peak of the roof runs along the length of the building or along the width of the building. I am going to assume that the peak runs along the length. Below is a cross-section of the building

The triangle with sides of length 5 and 12 is a right triangle and hence you can use the Theorem of Pythagoras to find the hypotenuse. 52 + 122 = 169 and 132 = 169 so the length of the hypotenuse is 13 feet. The roof extends 1.5 feet beyond the front and back walls so the roof is composed of two rectangular sides, each 40 feet by 14.5 feet. Thus you can find the area of the roof and hence the number of packs of shingles required.

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