What is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16 ft.?(1 point)
Responses
128 ft.2
128 ft. squared
512 ft.2512 ft. squared
256 ft.2256 ft. squared
320 ft.2
To find the surface area of a square pyramid, you need to calculate the area of the base and the area of the four triangular faces.
The area of a square base can be found by multiplying the length of one side by itself: 8 ft. x 8 ft. = 64 ft².
The area of each triangular face can be found using the formula: 1/2 x base x height.
The base of each triangular face is the length of one side of the square base, which is 8 ft.
The height of each triangular face can be found using the Pythagorean theorem. The height is the slant height of the pyramid, which is 16 ft. So, the height of each triangular face is the hypotenuse of a right triangle with one side of 8 ft (half the base of the square) and a height of 16 ft. Using the Pythagorean theorem, we can calculate the height of the triangle: h² = 16² - 8² = 256 - 64 = 192. Taking the square root of 192, we get h ≈ 13.86 ft.
The area of each triangular face is then: 1/2 x 8 ft. x 13.86 ft. = 55.44 ft².
Now, let's calculate the total surface area by adding up the areas of the base and the four triangular faces:
Base area: 64 ft²
Triangular face areas: 4 x 55.44 ft² = 221.76 ft²
Total surface area: 64 ft² + 221.76 ft² = 285.76 ft²
Therefore, the surface area of the square pyramid is approximately 285.76 ft².