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
251 square yards
276 square yards
1,298 square yards
To find the surface area of a square pyramid, you need to find the area of each face and then add them together. The formula for the surface area of a square pyramid is:
Surface area = base area + (1/2 * perimeter of base * slant height)
First, let's find the base area. The base of the pyramid is a square, so the area of the base is simply the length of one side squared. Since the base edge length is 5 yards, the base area is:
Base area = 5 yards * 5 yards = 25 square yards
Next, we need to find the slant height. The slant height can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (slant height in this case) is equal to the sum of the squares of the other two sides.
In this case, the slant height is the hypotenuse, the height is one of the other sides, and the base edge length is the other side. Let's call the slant height "s".
Using the Pythagorean theorem, we can solve for "s":
s^2 = 5^2 + 25^2
s^2 = 25 + 625
s^2 = 650
s ≈ 25.5 yards
Now, let's find the perimeter of the base. The base is a square, so all sides are equal. The perimeter of a square is simply 4 times the length of one side. Since the base edge length is 5 yards, the perimeter of the base is:
Perimeter of base = 4 * 5 yards = 20 yards
Finally, we can calculate the surface area of the square pyramid:
Surface area = 25 square yards + (1/2 * 20 yards * 25.5 yards)
Surface area = 25 + (0.5 * 20 * 25.5)
Surface area ≈ 276 square yards
Therefore, the surface area of the square pyramid is approximately 276 square yards.