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
512 ft.2512 ft. squared
320 ft.2
320 ft. squared
256 ft.2256 ft. squared
128 ft.2
The surface area of a square pyramid can be found by calculating the sum of the areas of the base and the four triangular faces.
First, calculate the area of the base. Since the base is a square, the area is equal to the length of one side squared. In this case, the base edge is 8 ft, so the area of the base is 8 ft * 8 ft = 64 ft^2.
Next, calculate the area of each triangular face. A triangular face is a right triangle, so we can use the formula for the area of a right triangle: (1/2) * base * height.
The base of each triangular face is the base edge of the pyramid, which is 8 ft. The height can be found by using the Pythagorean Theorem, which states that the square of the hypotenuse (the slant height) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is 16 ft, and one of the other sides is the base edge (8 ft). Let's call the other side "h".
Using the Pythagorean Theorem: 16 ft^2 = 8 ft^2 + h^2
Rearranging the equation: h^2 = 16 ft^2 - 8 ft^2 = 64 ft^2
Taking the square root of both sides: h = √(64 ft^2) = 8 ft
Therefore, the height of each triangular face is 8 ft, and the slant height is also 8 ft.
Now, we can calculate the area of each triangular face:
Area of each triangular face = (1/2) * base * height
= (1/2) * 8 ft * 8 ft
= 32 ft^2
Since there are four triangular faces, the total area of the triangular faces is 4 * 32 ft^2 = 128 ft^2.
The total surface area of the pyramid is the sum of the area of the base and the area of the triangular faces:
Total surface area = Base area + Triangular faces area
= 64 ft^2 + 128 ft^2
= 192 ft^2
Therefore, the surface area of the square pyramid is 192 ft^2.
The correct option is 192 ft^2.
use one of the options bot
Sure, the correct option is 192 ft^2.
use one of the options i gave you
The surface area of the square pyramid is 320 ft^2.
The correct option is 320 ft^2.