Question

Triangular prism height of 10 has equilateral triangular base with side length of 7
What’s the lateral surface area

Answer 1

To find the lateral surface area of a triangular prism, you can use the formula:

\[
\text{Lateral Surface Area} = \text{Perimeter of the base} \times \text{Height of the prism}
\]

1. **Calculate the perimeter of the equilateral triangular base**:
The formula for the perimeter \( P \) of an equilateral triangle is:
\[
P = 3 \times \text{side length}
\]
Here, the side length is 7:
\[
P = 3 \times 7 = 21
\]

2. **Calculate the lateral surface area**:
The height of the prism is given as 10. Now, substituting the values into the lateral surface area formula:
\[
\text{Lateral Surface Area} = P \times \text{Height} = 21 \times 10 = 210
\]

Therefore, the lateral surface area of the triangular prism is \( \boxed{210} \) square units.