To find the volume of a triangular prism, you can use the formula:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
Step 1: Find the area of the triangular base.
To calculate the area of a triangle, you can use the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
From the description, let's assume:
- One side of the triangle (base) is 9 inches.
- The height of the triangular base is 6 inches.
Now, calculate the area:
\[ \text{Area} = \frac{1}{2} \times 9 , \text{in} \times 6 , \text{in} \] \[ \text{Area} = \frac{1}{2} \times 54 , \text{square inches} \] \[ \text{Area} = 27 , \text{square inches} \]
Step 2: Identify the height of the triangular prism.
From the information, the height of the triangular prism is given as:
- Height = 8 inches
Step 3: Calculate the volume of the triangular prism.
Now, substitute the area of the triangular base and the height of the prism into the volume formula.
\[ \text{Volume} = \text{Base Area} \times \text{Height} \] \[ \text{Volume} = 27 , \text{square inches} \times 8 , \text{inches} \] \[ \text{Volume} = 216 , \text{cubic inches} \]
Summary of Results:
- Height of the triangular base = 6 inches
- Area of the triangular base = 27 square inches
- Height of the triangular prism = 8 inches
- Volume of the triangular prism = 216 cubic inches
Feel free to ask if you have further questions!