Question

what is the lateral surface area of a triangular prism with a length of 8cm, width of 6cm and height of 5cm

Answer 1

To find the lateral surface area of a triangular prism, we can follow these steps:

1. **Identify the dimensions**:
- Length of the prism (L) = 8 cm
- Base width of the triangle (b) = 6 cm
- Height of the triangle (h) = 5 cm

2. **Find the perimeter of the triangular base** (P):
For a triangular prism, we need to know the lengths of the sides of the triangular base. However, since we are given the width and height, we can assume it’s a right triangle for simplicity. We can calculate the hypotenuse (c) using the Pythagorean theorem:
\[
c = \sqrt{(b^2 + h^2)} = \sqrt{(6^2 + 5^2)} = \sqrt{36 + 25} = \sqrt{61} \approx 7.81 \, \text{cm}
\]

The perimeter \( P \) of this right triangle would then be:
\[
P = b + h + c = 6 + 5 + c = 6 + 5 + 7.81 = 18.81 \, \text{cm}
\]

3. **Calculate the lateral surface area (A_l)**:
The formula for the lateral surface area of a triangular prism is given by:
\[
A_l = P \times L
\]
Substituting the values we found:
\[
A_l = 18.81 \times 8 \approx 150.48 \, \text{cm}^2
\]

Therefore, the lateral surface area of the triangular prism is approximately **150.48 cm²**.