The formula for the surface area of a square pyramid is:
SA = (base area) + (4 * (base edge length * slant height) / 2)
In this case, the base edge length is 5 yards and the height is 25 yards. To find the surface area, we need to find the base area and the slant height.
The base area of a square is calculated by multiplying the base edge length by itself:
base area = (5 yd)^2 = 25 yd^2
The slant height can be found using the Pythagorean theorem. The slant height is the hypotenuse of a right triangle that is formed by the height, the base edge length, and half the base diagonal.
The base diagonal of a square can be found using the Pythagorean theorem:
diagonal = √(base edge length^2 + base edge length^2) = √(5 yd^2 + 5 yd^2) = √(25 yd^2 + 25 yd^2) = √(50 yd^2) = 5√2 yd
The slant height is half the base diagonal:
slant height = 5√2 yd / 2 = (5/2)√2 yd
Now we can substitute the values into the formula for the surface area of the square pyramid:
SA = base area + 4 * (base edge length * slant height) / 2
= 25 yd^2 + 4 * (5 yd * (5/2)√2 yd) / 2
= 25 yd^2 + 4 * (25/2)√2 yd^2 / 2
= 25 yd^2 + 50√2 yd^2
= 25 yd^2 + 50√2 yd^2
= 25 yd^2 + 50√2 yd^2
= 25 + 50√2 yd^2
Therefore, the surface area of the square pyramid is 25 + 50√2 square yards.
Use the formula for the surface area of a square pyramid on the surface area if the base edge length is 5 yards in the height is 25 yd
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