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

Answer 1

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.