how many square feet of shingles need to be replaced?

Question

A church steeple in the shape of a regular square pyramid needs to be reshingled. The part to be covered corresponds to the lateral area of the square pyramid. If each lateral edge measures 25 ft and each base edge measures 14 ft, how many square feet of shingles need to be replaced?

Answer 1

Sounds to be as if you have four equivalent isosceles triangles that need to be shingled. The two equal-length sides of each triangle are 25 feet. The third side of each triangle is 14 feet.

If you find the area of one triangle, you can multiply by four to find the square feet of shingles needed to shingle the entire roof of the steeple. The area of a triangle is one-half the base times the height. Half the base is 14/2 or 7.

Now, to find the height. If you drop a perpendicular from the vertex of the two long sides, you will create two new right triangles. That perpendicular is the height, and you can use the Pythagorean Theorem to find that height.

7^{2 +} h^{2 =} 25²

49 + h² = 625

h² = 625 – 49

h² = 576

h = 24

So, the area of one triangular side of the roof is 7 x 24 or 148 square feet.

Multiply 148 by four to get the amount of shingles to cover all four triangular sides of the roof. I get 592 square feet of shingles are needed to cover the church's steeple.

<Check my work. I did this by hand.>