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 SA equals 2,800 in2 .(1 point)
The formula for the surface area of a square pyramid is:
SA = (1/2) * p * l + B
Where SA is the surface area, p is the perimeter of the base, l is the slant height, and B is the area of the base.
Given that the length of the base is 40 in. and the SA equals 2,800 in^2, we can set up the equation:
2800 = (1/2) * 40 * l + B
To solve for the slant height, we need to find the perimeter of the base and the area of the base.
The perimeter of a square is given by:
p = 4 * side length
Since the base is a square, all sides are equal, so the perimeter can be calculated as:
p = 4 * 40 = 160 in.
The area of a square is given by:
B = side length^2
Since the base is a square, the area can be calculated as:
B = 40^2 = 1600 in^2
Substituting the values of p and B into the equation, we get:
2800 = (1/2) * 160 * l + 1600
Simplifying the equation:
2800 = 80l + 1600
Subtracting 1600 from both sides:
1200 = 80l
Dividing both sides by 80:
l = 15
Therefore, the slant height of the square pyramid is 15 inches.
The correct formula for finding the surface area of a regular triangular pyramid is:
SA = 1/2 * base * slant height + 3 * (1/2 * lateral edge * slant height)
where SA is the surface area, base is the area of the base (which is a triangle), slant height is the length of the slant height of the pyramid, and lateral edge is the length of the lateral edge of the pyramid.