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
151 square yards
151 square yards
1,298 square yards
1,298 square yards
276 square yards
276 square yards
251 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)
The base area of a square pyramid is the area of the square base. Since the base edge length is 5 yards, the base area would be 5 * 5 = 25 square yards.
Now, let's calculate the slant height. In a square pyramid, the slant height can be found using the Pythagorean Theorem. The slant height, s, can be found using the formula:
s = √(h^2 + (0.5 * base edge length)^2)
Substituting the given values:
s = √(25^2 + (0.5 * 5)^2)
s = √(625 + 6.25)
s = √631.25
s ≈ 25.14 yards
Next, let's calculate the perimeter of the base. Since the base is a square, all sides are equal. The perimeter of the base is 4 times the base edge length:
Perimeter of base = 4 * base edge length
Perimeter of base = 4 * 5
Perimeter of base = 20 yards
Now, we can calculate the surface area:
Surface Area = base area + (0.5 * perimeter of base * slant height)
Surface Area = 25 + (0.5 * 20 * 25.14)
Surface Area = 25 + (0.5 * 502.8)
Surface Area = 25 + 251.4
Surface Area ≈ 276 square yards
Therefore, the surface area of the square pyramid is approximately 276 square yards.