Question
Find the surface area of a square pyramid with a base length of 3 ft and a slant height of 8 ft
Answers
Answered by
GPT 3.5
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
The base of the pyramid is a square, so its area is found by squaring the length of one of its sides. In this case, the base length is 3 ft, so the area of the base is 3^2 = 9 sq ft.
To find the area of each triangular face, we need to find the area of a triangle. The formula for the area of a triangle is A = (1/2) × base × height. In this case, the base of the triangle is the length of one side of the square base, which is 3 ft. The height of the triangle is the slant height of the pyramid, which is 8 ft. Therefore, the area of each triangular face is (1/2) × 3 ft × 8 ft = 12 sq ft.
Since there are four triangular faces, the total area of the triangular faces is 4 × 12 sq ft = 48 sq ft.
Finally, to find the surface area of the square pyramid, we add the area of the base to the area of the triangular faces: 9 sq ft + 48 sq ft = 57 sq ft.
Therefore, the surface area of the square pyramid is 57 square feet.
The base of the pyramid is a square, so its area is found by squaring the length of one of its sides. In this case, the base length is 3 ft, so the area of the base is 3^2 = 9 sq ft.
To find the area of each triangular face, we need to find the area of a triangle. The formula for the area of a triangle is A = (1/2) × base × height. In this case, the base of the triangle is the length of one side of the square base, which is 3 ft. The height of the triangle is the slant height of the pyramid, which is 8 ft. Therefore, the area of each triangular face is (1/2) × 3 ft × 8 ft = 12 sq ft.
Since there are four triangular faces, the total area of the triangular faces is 4 × 12 sq ft = 48 sq ft.
Finally, to find the surface area of the square pyramid, we add the area of the base to the area of the triangular faces: 9 sq ft + 48 sq ft = 57 sq ft.
Therefore, the surface area of the square pyramid is 57 square feet.