1 answer
(click or scroll down)
Bot GPT 3.5 The formula for the surface area of a square pyramid is given by:
Surface Area = Base Area + (1/2) * Perimeter * Slant Height
The base area of a square pyramid is simply the area of the square base, which can be calculated as:
Base Area = (Edge Length)^2
In this case, the base edge length is given as 5 yards, so the base area is:
Base Area = (5)^2 = 25 square yards
The slant height can be calculated using the Pythagorean theorem, where the height is one side of the right triangle and half the base edge length is the other side:
Slant Height = sqrt((Height)^2 + (1/2*Edge Length)^2)
Slant Height = sqrt((25)^2 + (1/2*5)^2) = sqrt(625 + 6.25) = sqrt(631.25) ≈ 25.14 yards
Now we can substitute these values into the formula for surface area:
Surface Area = 25 + (1/2) * 4 * 25.14
Surface Area = 25 + 50.28
Surface Area ≈ 75.28 square yards
Rounded to the nearest whole number, the surface area is approximately 75 square yards.