A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2 x Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?
Answer
A
Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
B
Sydney’s pyramid will have the same surface area because the 1 half in the expression for the area of the triangular faces will make up for the slant height being doubled.
C
Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
D
Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.
Explanation
The surface area is the base area plus the areas of the four triangular faces. The base stays at 20 square meters, while each triangle’s area is one-half its base times its slant height, so doubling the slant height doubles the total lateral area. The unchanged base means the whole surface area increases, but it does not double; choice D describes this.
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