To find the surface area of a square pyramid, you can use the formula:
\[ \text{Surface Area} = \text{Base Area} + \text{Lateral Area} \]
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Calculate the base area: The base of the pyramid is a square with a side length of 8 ft.
\[ \text{Base Area} = \text{side}^2 = 8 , \text{ft} \times 8 , \text{ft} = 64 , \text{ft}^2 \]
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Calculate the lateral area: The lateral area of a square pyramid is given by:
\[ \text{Lateral Area} = \frac{1}{2} \times \text{Perimeter of the base} \times \text{slant height} \]
The perimeter of the base is:
\[ \text{Perimeter} = 4 \times \text{side} = 4 \times 8 , \text{ft} = 32 , \text{ft} \]
Now substituting the values into the lateral area formula:
\[ \text{Lateral Area} = \frac{1}{2} \times 32 , \text{ft} \times 16 , \text{ft} = 256 , \text{ft}^2 \]
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Total surface area: Now we can sum the base area and lateral area to find the total surface area:
\[ \text{Surface Area} = \text{Base Area} + \text{Lateral Area} = 64 , \text{ft}^2 + 256 , \text{ft}^2 = 320 , \text{ft}^2 \]
Thus, the surface area of the square pyramid is 320 ft² (or 320 ft. squared).