Final answer:
To find the surface area of a pyramid, we calculate the base area and add it to the product of half the perimeter of the base and the slant height. For this pyramid with a square base of side length 5 ft and a height of 3 ft, the surface area is approximately 29.58 ft².
Step-by-step explanation:
To find the surface area of a pyramid, we need to use the formula:
Surface Area = base area + (0.5 × perimeter of base × slant height)
In this case, the base of the pyramid is a square with side length 5 ft. So, the base area is 5 ft × 5 ft = 25 ft².
The slant height of the pyramid can be found using Pythagoras' theorem:
slant height² = height² + (0.5 × side length)²
slant height² = 3 ft² + (0.5 × 3 ft)²
slant height² = 3 ft² + 0.25 × 9 ft²
slant height² = 3 ft² + 2.25 ft²
slant height² = 5.25 ft²
slant height is the square root of 5.25 ft² = √5.25 ft ≈ 2.29 ft
Finally, we can calculate the surface area of the pyramid:
Surface Area = 25 ft² + (0.5 × 4 × 2.29 ft)
Surface Area ≈ 25 ft² + 4.58 ft²
Surface Area ≈ 29.58 ft²