Question

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

Answer 1

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.