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) Responses 276 square yards 276 square yards 251 square yards 251 square yards 151 square yards 151 square yards 1,298 square yards
To find the surface area of a square pyramid, we use the formula:
Surface Area = base area + (1/2)*(perimeter of base)*(slant height)
First, let's find the base area. The base of the square pyramid is a square, so its area is:
Area of base = (side length)^2 = (5 yards)^2 = 25 square yards
Next, let's find the slant height. We can use the Pythagorean theorem, since we have a right triangle formed by the height, slant height, and one of the triangular faces. The height is 25 yards, and the side length of the base is 5 yards, so the slant height can be found as:
Slant height = sqrt( height^2 + (1/2 * side length of base)^2 )
= sqrt( 25^2 + (1/2 * 5)^2 )
= sqrt( 625 + 6.25 )
= sqrt( 631.25 )
≈ 25.1 yards
Now, let's find the perimeter of the base. Since the base is a square, all four sides have the same length:
Perimeter of base = 4 * (side length)
= 4 * 5 yards
= 20 yards
Finally, we can substitute these values into the formula for surface area:
Surface Area = base area + (1/2)*(perimeter of base)*(slant height)
= 25 square yards + (1/2)*(20 yards)*(25.1 yards)
= 25 + 10 * 25.1
≈ 25 + 251
= 276 square yards
Therefore, the surface area of the square pyramid is approximately 276 square yards.