Asked by Evan
13 in
12 in
14 in
Use nets to find the surface area of the triangular pyramid with an equilateral base.
175 in.2
357 in.2
273 in.2
84 in.2
12 in
14 in
Use nets to find the surface area of the triangular pyramid with an equilateral base.
175 in.2
357 in.2
273 in.2
84 in.2
Answers
Answered by
GPT 3.5
To find the surface area of a triangular pyramid with an equilateral base, we first need to find the lateral area and the base area.
First, let's find the lateral area. The lateral faces of a pyramid are triangles, and the lateral area is equal to the area of all the lateral faces combined.
The lateral area of a triangular pyramid can be found using the formula:
Lateral area = 1/2 * perimeter of base * slant height
Since the base is an equilateral triangle, each side is 12 in long. The perimeter of the base is 3 * 12 = 36 in.
We are given that the slant height is 13 in. Therefore, the lateral area is: 1/2 * 36 * 13 = 234 in^2.
Next, let's find the base area. The base of the pyramid is an equilateral triangle.
The formula for the area of an equilateral triangle is:
Area = (sqrt(3) / 4) * side length^2
Plugging in the side length of 12 in, we get: Area = (sqrt(3) / 4) * 12^2 = 36sqrt(3) in^2.
Finally, we can find the total surface area by adding the lateral area and the base area:
Total surface area = lateral area + base area = 234 + 36sqrt(3) ≈ 273 in^2
Therefore, the surface area of the triangular pyramid with an equilateral base is approximately 273 in^2.
First, let's find the lateral area. The lateral faces of a pyramid are triangles, and the lateral area is equal to the area of all the lateral faces combined.
The lateral area of a triangular pyramid can be found using the formula:
Lateral area = 1/2 * perimeter of base * slant height
Since the base is an equilateral triangle, each side is 12 in long. The perimeter of the base is 3 * 12 = 36 in.
We are given that the slant height is 13 in. Therefore, the lateral area is: 1/2 * 36 * 13 = 234 in^2.
Next, let's find the base area. The base of the pyramid is an equilateral triangle.
The formula for the area of an equilateral triangle is:
Area = (sqrt(3) / 4) * side length^2
Plugging in the side length of 12 in, we get: Area = (sqrt(3) / 4) * 12^2 = 36sqrt(3) in^2.
Finally, we can find the total surface area by adding the lateral area and the base area:
Total surface area = lateral area + base area = 234 + 36sqrt(3) ≈ 273 in^2
Therefore, the surface area of the triangular pyramid with an equilateral base is approximately 273 in^2.