Determine the volume of the prism.
Understand the Problem
The question is asking to determine the volume of the given prism. We need to calculate the area of the triangular face, then multiply by the length of the prism to find the volume.
Answer
$192$
Answer for screen readers
$192$
Steps to Solve
- Calculate the area of the triangular face on the left
The formula for the area of a triangle is $A = \frac{1}{2} \cdot base \cdot height$.
In this case, the base of the triangle is 8 m and the height is 4 m.
$A = \frac{1}{2} \cdot 8 \cdot 4 = 16 \text{ m}^2$
- Multiply the area of the triangular face by the length of the prism
The length of the prism is 12 m. To find the volume, we multiply the area of the triangle by the length.
$V = 16 \cdot 12 = 192 \text{ m}^3$
$192$
More Information
The volume of the prism is 192 cubic meters.
Tips
A common mistake is confusing the different dimensions and using the wrong values for base, height, or length. It's important to correctly identify which sides correspond to which dimension in the formulas. Also, some might use the side length of 5m in the calculation which is not required.
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