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.
a 151 square yards
b 276 square yards
c 1,298 square yards
d 251 square yards
The formula for the surface area of a square pyramid is given by:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
In this case, the base edge length is 5 yards and the height is 25 yards.
The area of the base is equal to the length of one side squared, so we have:
Base Area = 5 yards * 5 yards = 25 square yards
Next, let's calculate the perimeter of the base. Since it is a square, all four sides have the same length, which is 5 yards. So, the perimeter is:
Perimeter of Base = 4 * 5 yards = 20 yards
Next, let's calculate the slant height. To do this, we can draw a right triangle using the height, half the base edge length, and the slant height as the hypotenuse.
Using the Pythagorean theorem, we have:
(0.5 * Base Edge Length)^2 + Height^2 = Slant Height^2
(0.5 * 5 yards)^2 + 25 yards^2 = Slant Height^2
2.5 yards^2 + 625 yards^2 = Slant Height^2
627.5 yards^2 = Slant Height^2
Slant Height ≈ square root of 627.5 ≈ 25.05 yards (rounding to two decimal places)
Now, let's substitute all these values into the formula:
Surface Area = 25 square yards + (0.5 * 20 yards * 25.05 yards)
Surface Area = 25 square yards + (0.5 * 500.5 square yards)
Surface Area ≈ 25 square yards + 250.25 square yards
Surface Area ≈ 275.25 square yards
Rounding to the nearest whole number, the surface area is approximately 275 square yards.
Therefore, the correct answer is b) 276 square yards.