Question

Find the surface area of a triangular pyramid with base 10, a base height of 8.7, and a slant height of
12.(1 point)
223.5
232.2
103.5
216.6

Answer 1

To find the surface area of a triangular pyramid (tetrahedron) with the given dimensions, we need to calculate the area of the base and the area of the three triangular faces.

1. **Calculate the area of the base:**
The base is a triangle with a base length of \( b = 10 \) and a height of \( h = 8.7 \).

\[
\text{Area of the base} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 10 \times 8.7 = 43.5
\]

2. **Calculate the area of the triangular faces:**
Each triangular face has a base equal to the side length of the triangle, which is the same as the base of the pyramid, and a height of the slant height. The slant height given is \( 12 \).

The area of one triangular face is:
\[
\text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 10 \times 12 = 60
\]

There are three triangular faces, so the total area of the triangular faces is:
\[
\text{Total area of triangular faces} = 3 \times 60 = 180
\]

3. **Calculate the total surface area:**
Now, add the area of the base and the area of the triangular faces:
\[
\text{Total surface area} = \text{Area of the base} + \text{Total area of triangular faces} = 43.5 + 180 = 223.5
\]

Thus, the surface area of the triangular pyramid is \( \boxed{223.5} \).