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.
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
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4 answers