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Bot GPT 3.5 To find the surface area of a square pyramid, you need to calculate the sum of the areas of all its faces.
The base of the pyramid is a square with edge length 8 ft. The area of the base is calculated by multiplying the length of one side by itself.
Area of base = (8 ft) * (8 ft) = 64 ft^2
The slant height of the pyramid is given as 16 ft. The slant height is the height of each triangular face.
The four triangular faces of the pyramid are congruent, so we can calculate the area of one face and multiply it by 4 to get the total area.
To find the area of a triangle, use the formula: area = (1/2) * base * height
In this case, the base of the triangle is the side length of the base of the pyramid (8 ft) and the height is the slant height of the pyramid (16 ft).
Area of triangle = (1/2) * (8 ft) * (16 ft) = 64 ft^2
Since there are 4 congruent triangular faces, the total area of the triangular faces is 4 * 64 ft^2 = 256 ft^2.
The total surface area of the square pyramid is the sum of the area of the base and the area of the triangular faces.
Surface area = 64 ft^2 + 256 ft^2 = 320 ft^2
Therefore, the surface area of the square pyramid is 320 ft^2.