To find the surface area of a square pyramid, you can use the formula:
\[ \text{Surface Area} = \text{Base Area} + \text{Lateral Area} \]
- Base Area: Since the base is a square with each edge measuring 8 ft, the area of the base is:
\[ \text{Base Area} = \text{side}^2 = 8 , \text{ft} \times 8 , \text{ft} = 64 , \text{ft}^2 \]
- Lateral Area: The lateral area consists of four triangular faces. The area of one triangular face can be calculated using the formula:
\[ \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base of each triangle is the same as the base of the pyramid (8 ft) and the height of each triangle is the slant height (16 ft). Therefore, the area of one triangular face is:
\[ \text{Area of one triangle} = \frac{1}{2} \times 8 , \text{ft} \times 16 , \text{ft} = 64 , \text{ft}^2 \]
Since there are four triangles, the total lateral area is:
\[ \text{Lateral Area} = 4 \times 64 , \text{ft}^2 = 256 , \text{ft}^2 \]
- Total Surface Area: Now, we add the base area to the lateral area:
\[ \text{Surface Area} = \text{Base Area} + \text{Lateral Area} = 64 , \text{ft}^2 + 256 , \text{ft}^2 = 320 , \text{ft}^2 \]
Therefore, the surface area of the square pyramid is 320 ft².
From your provided options, the correct response is 320 ft.².
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