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.
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
1 answer