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 po
The formula for the surface area of a square pyramid is:
SA = base_area + (1/2) * perimeter_of_base * slant_height
Given that the length of the base is 40 in. and the surface area is 2,800 in², we can substitute these values into the formula:
2,800 = base_area + (1/2) * perimeter_of_base * slant_height
To find the base area, we use the formula for the area of a square:
base_area = length_of_base * length_of_base
base_area = 40 * 40 = 1600 in²
Now, we can substitute this value into the equation:
2,800 = 1600 + (1/2) * perimeter_of_base * slant_height
To find the perimeter of the base, we use the formula for the perimeter of a square:
perimeter_of_base = 4 * length_of_base
perimeter_of_base = 4 * 40 = 160 in
Substituting this value into the equation:
2,800 = 1600 + (1/2) * 160 * slant_height
Now, we can simplify the equation:
2,800 - 1600 = 80 * slant_height
1,200 = 80 * slant_height
Dividing both sides of the equation by 80:
15 = slant_height
Therefore, the slant height of the square pyramid is 15 inches.