Question

Lateral Surface area of triangular prism with top and bottom bases of 5, rectangular faces of 6 and length of 8

Answer 1

To determine the lateral surface area of a triangular prism, you need to consider only the sides of the prism, which are the rectangular faces connecting the triangular bases. The lateral surface area can be calculated using the formula:

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

In your case, you mentioned that the top and bottom bases of the prism are triangles with a base of length 5. However, you didn't provide enough detail to determine the shape of the triangular base (specifically, its height). Nevertheless, you mentioned rectangular faces of length 6, which seems to imply the height of the prism is 6 (the height between the two triangular bases), and the length of the prism is 8.

### Steps to Calculate the Lateral Surface Area:

1. **Identify the dimensions**:
- Each triangular base has a base of 5.
- The length of the prism (the height between the triangular bases) is 8.
- You need the height of the triangular base to calculate its perimeter.

2. **Determine the perimeter of the triangular base**:
- If we assume that the triangular base is a right triangle where the height from the base to the apex is needed, we can calculate its perimeter once its sides are known. If additional dimensions are provided (like the lengths of the other two sides), we could get the complete perimeter.

Let's assume the triangular base is an isosceles triangle with both the other sides equal to 5 units (just as an example):
- Let's denote the sides as \( a = 5 \), \( b = 5 \), and \( c = 5 \).
- The perimeter \( P \) would then be \( P = a + b + c = 5 + 5 + 5 = 15 \).

3. **Calculate the lateral surface area**:
- Using the assumed perimeter:
\[
\text{Lateral Surface Area} = \text{Perimeter} \times \text{Height}
\]
\[
\text{Lateral Surface Area} = 15 \times 8 = 120
\]

### Conclusion:
Thus, the lateral surface area of this triangular prism, under the assumption of an equilateral triangle base (or similar interpretation based on the dimensions given), is \( 120 \) square units.

### Note:
Please provide the exact dimensions of the triangular base if available for a precise calculation.