exploringm wrote:
A pyramid with four equal-sized flat surfaces and a base of 36 ft2 has a height of 10 feet. What is the total surface area of the pyramid, excluding the base?
12 31^1/2
12 109^1/2
24 31^1/2
24 109^1/2
48 31^1/2
the book's answer description sort of says it's a right triangle without really explaining how we know that..can anyone help out with understanding that as well?
The total surface area of the pyramid, excluding the base, is also known as the lateral surface area of the pyramid. It is the total area of the 4 triangular faces of the pyramid.
Since the base of the pyramid is 36 ft^2, a side of the base is 6 ft. Recall that the height of the pyramid, half of a side of the base and the slant height of the pyramid form the three sides of a right triangle where the slant height is the hypotenuse. Since the height of the pyramid is 10 ft, half of a side of the base is 3 ft, so the slant height, s, can be determined by the equation:
10^2 + 3^2 = s^2
109 = s^2
s = 109^½
Recall that the slant height of the pyramid is also the height of the triangular faces of the pyramid, and a side of the base of the pyramid is the base of the triangular faces. So a triangular face has height = 109^½ and base = 6 and hence an area of 1/2 x 6 x 109^½ = 3 x 109^½. Since there are 4 triangular faces, the total area is 4 x 3 x 109^½ = 12 x 109^½.
Answer: B
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