Question

surface area of a triangular prism
width of 9
length of 6
height of 8

Answer 1

To calculate the surface area of a triangular prism, you will need to find both the lateral surface area and the area of the two triangular bases. Given that you have the width, length, and height, we'll assume the following:

- The base of the triangular cross-section is the width (9 units).
- The height of the triangular cross-section is the height (8 units).
- The length of the prism is 6 units.

### Step 1: Calculate the area of the triangular bases

The area \( A \) of one triangular base can be calculated using the formula for the area of a triangle:

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

Here, the base is 9 and the height is 8:

\[
A = \frac{1}{2} \times 9 \times 8 = \frac{1}{2} \times 72 = 36 \text{ square units}
\]

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

\[
\text{Total area of bases} = 2 \times 36 = 72 \text{ square units}
\]

### Step 2: Calculate the lateral surface area

The lateral surface area consists of three rectangular sides. The dimensions of each rectangle are:

1. Two rectangles with dimensions of length (6 units) and height (8 units).
2. One rectangle with dimensions of length (6 units) and base (9 units).

Now, calculate each rectangle's area:

1. Area of the two rectangles (6 by 8):

\[
\text{Area}_1 = 2 \times (6 \times 8) = 2 \times 48 = 96 \text{ square units}
\]

2. Area of the rectangle (6 by 9):

\[
\text{Area}_2 = 6 \times 9 = 54 \text{ square units}
\]

### Step 3: Combine areas to find total surface area

Add the areas of the triangular bases and the lateral surface area:

\[
\text{Total Surface Area} = \text{Area of bases} + \text{Lateral Surface Area}
\]

\[
\text{Total Surface Area} = 72 + (96 + 54) = 72 + 150 = 222 \text{ square units}
\]

### Final Answer

The total surface area of the triangular prism is \( 222 \) square units.