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) Responses 223.5 223.5 - no response given 103.5 103.5 - no response given 216.6 216.6 - no response given 232.2

Answer 1

To find the surface area of a triangular pyramid (also known as a tetrahedron), we need to calculate the area of its base and the areas of its three triangular faces.

1. **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. **Area of the triangular faces**: Each triangular face has a base of length \( b = 10 \) and a slant height \( l = 12 \). The area of one triangular face is calculated as follows:
\[
\text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 10 \times 12 = 60
\]
Since there are three triangular faces, the total area for all three faces is:
\[
\text{Total area of triangular faces} = 3 \times 60 = 180
\]

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

Hence, the surface area of the triangular pyramid is **223.5 square units**.