Use the formula for the surface area of a square pyramid to find the surface area of the base edge length is five and the height is 25 round to the nearest whole number
The formula for the surface area of a square pyramid is:
Surface Area = Base Area + (½ × Base Edge Length × Slant Height)
Given: Base Edge Length = 5 and Height = 25
First, we need to find the slant height. Since it is not given directly, we can use the Pythagorean theorem to calculate it. The slant height (l) can be found by:
l = √(h^2 + (0.5e)^2)
Where h is the height and e is the base edge length.
Substituting the given values:
l = √(25^2 + (0.5 × 5)^2)
= √(625 + 12.5)
= √637.5
≈ 25.24 (rounding to hundredths)
Now, we can calculate the surface area by substituting the values into the formula:
Surface Area = 5^2 + (0.5 × 5 × 25.24)
= 25 + (0.5 × 5 × 25.24)
= 25 + (0.5 × 126.2)
= 25 + 63.1
= 88.1
Rounding to the nearest whole number, the surface area of the square pyramid is approximately 88 square units.