Final answer:
To find the surface area of a regular pyramid, calculate the area of the base and the area of the lateral faces and then add them together using the formula Surface Area = Base Area + (1/2 × Perimeter of Base × Slant Height). For a pyramid with a base side length of 9ft and a slant height of 6ft, the surface area is 189ft².
Step-by-step explanation:
To find the surface area of a regular pyramid, you need to find the area of the base and the area of the lateral faces and then add them together. The formula for the surface area of a regular pyramid is:
Surface Area = Base Area + (1/2 × Perimeter of Base × Slant Height)
Given that the base of the pyramid has a side length of 9ft and the slant height is 6ft, we can calculate the surface area as follows:
- Base Area = (side length)² = (9ft)² = 81ft²
- Perimeter of Base = 4 × (side length) = 4 × 9ft = 36ft
- Surface Area = 81ft² + (1/2 × 36ft × 6ft) = 81ft² + 108ft² = 189ft²