Question

How do you calculate the area of a triangular prism?

Answer 1

To calculate the surface area of a triangular prism, you need to consider both the area of its triangular bases and the area of its three rectangular lateral faces. Here’s how to do it step-by-step:

1. **Calculate the area of the triangular base**:
If the triangle has a base \( b \) and a height \( h \), the area \( A_{triangle} \) is calculated using the formula:
\[
A_{triangle} = \frac{1}{2} \times b \times h
\]

2. **Find the perimeter of the triangular base**:
If the sides of the triangle are \( a \), \( b \), and \( c \), the perimeter \( P \) is:
\[
P = a + b + c
\]

3. **Calculate the area of the lateral faces**:
The lateral faces are rectangles. Each rectangle's area can be found by multiplying the height of the prism \( H \) by the length of the sides of the triangle:
- The area of the rectangle corresponding to side \( a \) is \( a \times H \),
- The area of the rectangle corresponding to side \( b \) is \( b \times H \),
- The area of the rectangle corresponding to side \( c \) is \( c \times H \).

The total area of the lateral faces \( A_{lateral} \) is:
\[
A_{lateral} = H \times P
\]

4. **Combine the areas**:
The total surface area \( A_{total} \) of the triangular prism is the sum of the area of the two triangular bases and the area of the lateral faces:
\[
A_{total} = 2 \times A_{triangle} + A_{lateral}
\]

Putting it all together, the final formula for the surface area of the triangular prism is:
\[
A_{total} = 2 \left( \frac{1}{2} \times b \times h \right) + H \times P
\]
This simplifies to:
\[
A_{total} = b \times h + H \times P
\]

Now you can plug in the values for \( b \), \( h \), \( H \), \( a \), \( b \), and \( c \) to calculate the surface area of the triangular prism.