A chocolate dessert is in the shape of a square pyramid. The pyramid is represented with
a net. How many square inches of icing are needed for the faces of the dessert?
(1 point)
60 in.
2
30 in.
2
39 in.
2
69 in.
2
The net of a square pyramid consists of a square base and four triangular faces. Since we are looking for the total amount of icing needed for all the faces, we need to calculate the sum of the areas of all these faces.
The formula for the area of a square is side^2, and for a triangle, it is (1/2) * base * height.
If we assume the sides of the square base are each 6 inches, then the area of the square base is 6^2 = 36 in^2.
The area of each triangular face can be calculated by using the Pythagorean theorem to find the slant height (l) of the pyramid: l = sqrt(3^2 + 6^2) = sqrt(45) = 3*sqrt(5) inches. Therefore, the area of one triangular face is (1/2) * 6 * 3*sqrt(5) = 9*sqrt(5) sq. in.
Since there are four triangular faces, the total area of the icing needed for the faces of the dessert is 36 (base) + 4(9*sqrt(5)) = 36 + 36*sqrt(5) = 36(1 + sqrt(5)) = 141.58 ~ 142 in^2.
Therefore, none of the provided options are correct. The closest option is 140 in^2, but this was not part of the choices provided.