Question

Use the formula of a surface area of a square pyramid to the surface area if the base edge length is 5 yards in the height is 25 yards around the nearest whole number

Answer 1

[AI-generated answer — Bot GPT 3.5]

The surface area of a square pyramid is given by the formula:

SA = Base Area + (½ × Perimeter of Base × Slant Height)

Given that the base edge length is 5 yards and the height is 25 yards, we can find the slant height by using the Pythagorean theorem. In a right triangle formed by the height, slant height, and half the base edge length, we have:

Slant Height^2 = Height^2 + (½ × Base Edge Length)^2

Slant Height^2 = 25^2 + (½ × 5)^2

Slant Height^2 = 625 + 6.25

Slant Height^2 = 631.25

Slant Height ≈ √(631.25) ≈ 25.13 yards

Now we can calculate the surface area:

SA = Base Area + (½ × Perimeter of Base × Slant Height)

The base area is simply the area of the square formed by the base edge length:

Base Area = (Base Edge Length)^2 = (5)^2 = 25 square yards

The perimeter of the base is given by 4 times the base edge length:

Perimeter of Base = 4 × Base Edge Length = 4 × 5 = 20 yards

Plugging these values into the surface area formula:

SA = 25 + (½ × 20 × 25.13)

SA = 25 + (10 × 25.13)

SA = 25 + 251.3

SA ≈ 276.3 square yards

Therefore, the surface area of the square pyramid is approximately 276.3 square yards.