use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40 in and S A equals 2,800 in^2
The formula for the surface area of a square pyramid is given by:
SA = l^2 + 2l * sl,
where l is the length of the base and sl is the slant height.
In this case, we are given that the length of the base is 40 in and the surface area is 2,800 in^2. Plugging these values into the formula, we get:
2800 = 40^2 + 2 * 40 * sl
Simplifying the equation, we have:
2800 = 1600 + 80 * sl
Subtracting 1600 from both sides:
1200 = 80 * sl
Dividing both sides by 80:
sl = 1200/80
sl = 15
Therefore, the slant height is 15 inches.