Question

Use the formula for the surface area of a square pyramid to find the surface area if the base edge length is 5 yards and the height is 25 yards. Round to the nearest whole number

Answer 1

The formula for the surface area of a square pyramid is

Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height.

First, we need to find the base area. Since the pyramid has a square base, the base area is just the side length squared. So, the base area is 5 yards squared.

Next, we need to find the perimeter of the base. Since the base is a square, all sides are equal in length. The perimeter of a square is 4 times the length of one side. So, the perimeter of the base is 4 * 5 = 20 yards.

Lastly, we need to find the slant height. The slant height is the distance from the top vertex of the pyramid to the midpoint of one of the sides of the base. We can use the Pythagorean theorem to calculate the slant height. The height of the pyramid forms a right triangle with the slant height as the hypotenuse and half the base length as one of the legs. So, we can use the Pythagorean theorem:

slant height squared = height squared + (1/2 * base length) squared
slant height squared = 25 squared + (1/2 * 5) squared
slant height squared = 625 + 6.25
slant height squared = 631.25
slant height ≈ 25.12 yards

Now, we can substitute these values into the surface area formula:

Surface Area = 5 + (1/2) * 20 * 25.12
Surface Area = 5 + 10 * 25.12
Surface Area = 5 + 251.2
Surface Area ≈ 256.2

Therefore, the surface area of the square pyramid is approximately 256 square yards.