A pyramid has a square base of side length 10cm and a height of 15cm. What is the surface area of the pyramid?

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Step:1 ：(text{Surface area of a pyramid} = text{Base area} + frac{1}{2}times text{Perimeter of base} timestext{Slant height})Step:2 ：(text{First, calculate the base area: } A_{base} = s^2 = 10^2 = 100cm^2)Step:3 ：(text{Next, calculate the slant height using the Pythagorean theorem: } s_{l} = sqrt{h^2 + (frac{s}{2})^2} = sqrt{15^2 + (frac{10}{2})^2} = sqrt{225 + 25} = sqrt{250} = 15.81cm)Step:4 ：(text{Finally, calculate the surface area: } A_{pyramid} = A_{base} + frac{1}{2}times text{Perimeter of base} timestext{s_{l}} = 100cm^2 + frac{1}{2} times 4 times 10cm times 15.81cm = 100cm^2 + 316.2cm^2)

Answer

Step: 1 ：(text{Surface area of a pyramid} = text{Base area} + frac{1}{2}times text{Perimeter of base} timestext{Slant height})Step: 2 ：(text{First, calculate the base area: } A_{base} = s^2 = 10^2 = 100cm^2)Step: 3 ：(text{Next, calculate the slant height using the Pythagorean theorem: } s_{l} = sqrt{h^2 + (frac{s}{2})^2} = sqrt{15^2 + (frac{10}{2})^2} = sqrt{225 + 25} = sqrt{250} = 15.81cm)Step: 4 ：(text{Finally, calculate the surface area: } A_{pyramid} = A_{base} + frac{1}{2}times text{Perimeter of base} timestext{s_{l}} = 100cm^2 + frac{1}{2} times 4 times 10cm times 15.81cm = 100cm^2 + 316.2cm^2)

A pyramid has a square base of side length 10cm and a height of 15cm. What is the surface area of the pyramid?

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