Question
9.9ft 15ft
Solve for the surface area of the square pyramid
522ft
819ft
299.25 ft
148.5 fr
Solve for the surface area of the square pyramid
522ft
819ft
299.25 ft
148.5 fr
Answers
Answered by
GPT 3.5
To solve for the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
1. Area of the base:
Given that the base is a square, we can calculate the area by squaring one of the sides.
Base Area = (Side)^2 = (9.9ft)^2 = 98.01ft^2
2. Area of the triangular faces:
Since the pyramid is a square pyramid, the triangular faces are all identical. Each triangular face is an isosceles triangle with a base length equal to the side length of the square base (9.9ft) and a height equal to the slant height of the pyramid (15ft).
Area of each triangular face = 0.5 * Base * Height
Area of each triangular face = 0.5 * 9.9ft * 15ft = 74.25ft^2
Total surface area of the pyramid:
Surface Area = Base Area + 4(Triangular Face Area)
Surface Area = 98.01ft^2 + 4(74.25ft^2)
Surface Area = 98.01ft^2 + 297ft^2
Surface Area = 395.01ft^2
Therefore, the surface area of the square pyramid is 395.01ft^2.
1. Area of the base:
Given that the base is a square, we can calculate the area by squaring one of the sides.
Base Area = (Side)^2 = (9.9ft)^2 = 98.01ft^2
2. Area of the triangular faces:
Since the pyramid is a square pyramid, the triangular faces are all identical. Each triangular face is an isosceles triangle with a base length equal to the side length of the square base (9.9ft) and a height equal to the slant height of the pyramid (15ft).
Area of each triangular face = 0.5 * Base * Height
Area of each triangular face = 0.5 * 9.9ft * 15ft = 74.25ft^2
Total surface area of the pyramid:
Surface Area = Base Area + 4(Triangular Face Area)
Surface Area = 98.01ft^2 + 4(74.25ft^2)
Surface Area = 98.01ft^2 + 297ft^2
Surface Area = 395.01ft^2
Therefore, the surface area of the square pyramid is 395.01ft^2.