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 can use the formula:
Surface Area = base area + (0.5 * perimeter of base * slant height)
First, let's calculate the base area:
Base Area = base edge length^2
Base Area = 5^2
Base Area = 25 square yards
Next, let's calculate the perimeter of the base:
Perimeter of Base = 4 * base edge length
Perimeter of Base = 4 * 5
Perimeter of Base = 20 yards
Next, let's calculate the slant height:
Slant Height = square root of ( (0.5 * base edge length)^2 + height^2 )
Slant Height = square root of ( (0.5 * 5)^2 + 25^2 )
Slant Height = square root of ( 2.5^2 + 625 )
Slant Height = square root of ( 6.25 + 625 )
Slant Height = square root of 631.25
Slant Height ≈ 25.12 yards
Now, let's plug these values into the formula for the surface area:
Surface Area = 25 + (0.5 * 20 * 25.12)
Surface Area = 25 + (0.5 * 502.4)
Surface Area = 25 + 251.2
Surface Area ≈ 276.2 square yards
Rounded to the nearest whole number, the surface area of the square pyramid is approximately 276 square yards.