Question

Surface area of triangular prism with top and bottom bases of 5, rectangular faces of 6 and length of 15 and height of 4

Answer 1

To find the surface area of a triangular prism, we need to calculate the area of the triangular bases and the rectangular lateral faces.

1. **Area of the Triangular Base**:
The base of the triangular face is given as 5, and the height of the triangle is given as 4. The area \( A \) of a triangle is calculated using the formula:

\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

Substituting the values:

\[
A = \frac{1}{2} \times 5 \times 4 = \frac{20}{2} = 10
\]

Since there are two triangular bases, the total area of the triangular bases is:

\[
\text{Area of both triangular bases} = 2 \times A = 2 \times 10 = 20
\]

2. **Area of the Rectangular Faces**:
The prism has three rectangular faces, based on the dimensions provided:
- Two rectangles with base \( b = 5 \) and height \( h = 6 \) (the lengths of the sides of the triangle).
- One rectangle with height \( 4 \) and length \( 15 \) (the length of the prism).

First, calculate the area of the two rectangular faces that are connected to the triangular base:

\[
\text{Area of the two rectangular faces} = 2 \times (5 \times 6) = 2 \times 30 = 60
\]

Then, calculate the area of the rectangular face that is the length of the prism (with dimensions 4 and 15):

\[
\text{Area of the rectangular face} = 4 \times 15 = 60
\]

3. **Total Surface Area**:
Now, we can add all the areas together to find the total surface area of the prism:

\[
\text{Total Surface Area} = \text{Area of triangular bases} + \text{Area of rectangular faces}
\]
\[
\text{Total Surface Area} = 20 + 60 + 60 = 140
\]

Thus, the surface area of the triangular prism is \( \boxed{140} \).