The surface area (SA) of a square pyramid can be calculated using the formula:
\[ SA = B + \frac{1}{2}Pl \]
where:
- \( B \) is the area of the base,
- \( P \) is the perimeter of the base,
- \( l \) is the slant height.
Given that the length of the base \( a = 40 \) inches:
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Calculate the area of the base \( B \): \[ B = a^2 = 40^2 = 1600 \text{ in}^2 \]
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Calculate the perimeter \( P \) of the base: \[ P = 4a = 4 \times 40 = 160 \text{ in} \]
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You are given that the surface area \( SA = 2800 \text{ in}^2 \).
Now, plug these values into the surface area formula and solve for slant height \( l \):
\[ 2800 = 1600 + \frac{1}{2}(160)l \]
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Simplify the equation: \[ 2800 = 1600 + 80l \]
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Subtract 1600 from both sides: \[ 1200 = 80l \]
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Solve for \( l \): \[ l = \frac{1200}{80} = 15 \text{ in} \]
Thus, the slant height is \( 15 \) inches.