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. (1 point) 251 square yards 1,298 square yards 151 square yards 276 square yards
The formula for the surface area of a square pyramid is:
Surface area = base area + (1/2)(perimeter of base)(slant height)
First, let's calculate the base area:
The base of the square pyramid is a square, so the base area is equal to the side length squared.
Base area = 5 yards * 5 yards = 25 square yards
Next, let's calculate the perimeter of the base:
The perimeter of a square is equal to 4 times the side length.
Perimeter of base = 4 * 5 yards = 20 yards
Finally, let's calculate the slant height:
The slant height can be found using the Pythagorean theorem.
The slant height is the height of the triangle formed by one of the triangular faces, and the hypotenuse of that triangle is the slant height.
Using the Pythagorean theorem:
slant height^2 = height^2 + (base edge length/2)^2
slant height^2 = 25 yards^2 + (5 yards/2)^2
slant height^2 = 625 yards^2 + 6.25 square yards
slant height = √(625 yards^2 + 6.25 square yards)
slant height ≈ 25.02 yards (rounded to two decimal places)
Now we can plug the values into the formula for surface area:
Surface area = 25 square yards + (1/2)(20 yards)(25.02 yards)
Surface area = 25 square yards + 500.4 square yards
Surface area ≈ 525.4 square yards
Rounded to the nearest whole number, the surface area is 525 square yards.
So, the correct answer is: 525 square yards