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Find the surface area of a square pyramid with side length 3 m and slant height 6 m.

Find the surface area of a square pyramid with side length 3 m and slant height 6 m-example-1
User Duessi
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The surface area of the square pyramid is 45 square meters.



To find the surface area of a square pyramid, we need to calculate the area of the base and the four triangular faces.

Given a square pyramid with a side length of 3 meters and a slant height of 6 meters:

Calculate the base area (square):
Side length = 3 m
Base area = side length² = 3² = 9 m²
Calculate the area of one triangular face:
Base of the triangle (same as the side length of the square base) = 3 m
Slant height = 6 m
Area of one triangular face = 0.5 * base * height = 0.5 * 3 * 6 = 9 m²
Since there are four triangular faces, we multiply the area of one face by 4:
Total area of all triangular faces = 4 * 9 = 36 m²
Add the base area and the total area of the triangular faces to get the surface area of the square pyramid:
Surface area = Base area + Total area of triangular faces = 9 + 36 = 45 m²
User Zoltan Balazs
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