A pyramid has a square base of side length 4 cm. Each of the triangular faces has a height of 6 cm. What is the surface area of the pyramid?

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Accepted Answer

Step:1 ：The surface area of a pyramid is given by the formula (A = B + frac{1}{2}Psl), where (B) is the area of the base, (P) is the perimeter of the base, and (sl) is the slant height. In this case, the base is a square, so (B = s^2) and (P = 4s), where (s) is the side length of the base. The slant height is the height of the triangular faces, which we&#x27;ll call (h_t).Step:2 ：First, we calculate the area of the base: (B = s^2 = 4^2 = 16 , cm^2).Step:3 ：Next, we calculate the perimeter of the base: (P = 4s = 4 times 4 = 16 , cm).Step:4 ：Now we can find the surface area of the pyramid: (A = B + frac{1}{2}Psl = 16 + frac{1}{2} times 16 times 6 = 16 + 48 = 64 , cm^2).

Answer

Step: 1 ：The surface area of a pyramid is given by the formula (A = B + frac{1}{2}Psl), where (B) is the area of the base, (P) is the perimeter of the base, and (sl) is the slant height. In this case, the base is a square, so (B = s^2) and (P = 4s), where (s) is the side length of the base. The slant height is the height of the triangular faces, which we&#x27;ll call (h_t).Step: 2 ：First, we calculate the area of the base: (B = s^2 = 4^2 = 16 , cm^2).Step: 3 ：Next, we calculate the perimeter of the base: (P = 4s = 4 times 4 = 16 , cm).Step: 4 ：Now we can find the surface area of the pyramid: (A = B + frac{1}{2}Psl = 16 + frac{1}{2} times 16 times 6 = 16 + 48 = 64 , cm^2).

A pyramid has a square base of side length 4 cm. Each of the triangular faces has a height of 6 cm. What is the surface area of the pyramid?

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