Question

what is the lateral surface area of a triangular prism with a lateral edge of 8cm, base of 6cm and equal sides of 5cm each

Answer 1

To find the lateral surface area of a triangular prism, we need to first determine the perimeter of the triangular base and then multiply it by the height of the prism.

1. **Identify the base of the triangle:**
The triangular base has sides of:
- Base = 6 cm
- Equal sides = 5 cm each

2. **Calculate the perimeter of the triangular base:**
\[
\text{Perimeter} = 6 + 5 + 5 = 16 \text{ cm}
\]

3. **Determine the height of the triangular prism (lateral edge):**
The lateral edge given is 8 cm. This is the height of the prism.

4. **Calculate the lateral surface area:**
The lateral surface area (LSA) of a prism can be calculated using the formula:
\[
LSA = \text{Perimeter of the base} \times \text{Height of the prism}
\]
Substituting the values we found:
\[
LSA = 16 \text{ cm} \times 8 \text{ cm} = 128 \text{ cm}^2
\]

Thus, the lateral surface area of the triangular prism is **128 cm²**.