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find the surface area of square pyramid with base edges of 8 feet the height of each lateral is 9 feet

Sagot :

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Explanations:

The surface area of a square based pyramid is given by the formula:

[tex]\begin{gathered} A\text{ = }a^2+2a\sqrt[]{\frac{a^2}{4}+h^2}^{} \\ \text{Where a = base edge } \\ h\text{ = lateral height} \end{gathered}[/tex]

From the question:

a = 8 feet

h = 9 feet

Substitute the values of a and h into the given formula for surface area:

[tex]\begin{gathered} A=8^2+2(8)\sqrt[]{\frac{8^2}{4}+9^2} \\ A\text{ = 64 + 16}\sqrt[]{\frac{64}{4}+81} \\ A\text{ = 64 + 16}\sqrt[]{16+81} \\ A\text{ = 64+16}\sqrt[]{97} \\ A\text{ =}64+157.58 \\ A\text{ = }221.58ft^2 \end{gathered}[/tex]

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