Question

How do you calculate the surface area of a triangular prism?

Answer 1

To calculate the surface area of a triangular prism, you need to find the area of the two triangular bases and the three rectangular faces that connect them.

Here’s a step-by-step approach:

1. **Identify dimensions:**
- Let the base of the triangular prism have a triangular base with a base length \( b \), height \( h \), and the lengths of the two other sides be \( a \) and \( c \).
- Let the length (or height) of the prism be \( L \).

2. **Calculate the area of the triangular base:**
The area \( A \) of the triangular base can be calculated using the formula:
\[
A = \frac{1}{2} \times b \times h
\]

3. **Calculate the area of the three rectangular faces:**
- The area of the rectangle connecting side \( a \) is given by \( A_1 = a \times L \).
- The area of the rectangle connecting side \( b \) is given by \( A_2 = b \times L \).
- The area of the rectangle connecting side \( c \) is given by \( A_3 = c \times L \).

4. **Total surface area calculation:**
The total surface area \( SA \) of the prism is calculated by adding the areas of the two triangular bases and the three rectangular faces:
\[
SA = 2A + A_1 + A_2 + A_3
\]
Plugging in the area formulas gives:
\[
SA = 2 \left(\frac{1}{2} \times b \times h\right) + (a \times L) + (b \times L) + (c \times L)
\]
Simplifying further:
\[
SA = b \times h + (a + b + c) \times L
\]

5. **Final formula:**
Thus, the total surface area of the triangular prism can be expressed as:
\[
SA = b \times h + (a + b + c) \times L
\]

Make sure to have all dimensions in consistent units before performing the calculations.