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 yardsRound to the nearest whole number ( 1 point)
The surface area of a square pyramid can be found using the formula:
Surface Area = Base Area + (1/2 * Perimeter of Base * Slant Height)
The base edge length is given as 5 yards, so the base area is 5^2 = 25 square yards.
To find the slant height, we can use the Pythagorean theorem:
h^2 = s^2 + (1/2 * e)^2, where h is the height, s is the slant height, and e is the base edge length.
Substituting the given values:
25^2 = s^2 + (1/2 * 5)^2
625 = s^2 + 6.25
s^2 = 618.75
s ≈ 24.85 yards (rounded to two decimal places)
The perimeter of the base is 4 * 5 = 20 yards.
Now we can substitute all these values into the surface area formula:
Surface Area = 25 + (1/2 * 20 * 24.85)
Surface Area ≈ 25 + (1/2 * 20 * 24.85)
Surface Area ≈ 25 + 248.5
Surface Area ≈ 273.5
Rounding to the nearest whole number, the surface area of the square pyramid is 274 square yards.