Anya hung up a decorative shelf in the shape of a triangular prism in her bathroom. The diagram shows the dimensions of the shelf.
Note: Figure is not drawn to scale.
What is the volume of the shelf?
To find the volume of the triangular prism shelf, we need to calculate the area of the triangular base and multiply it by the height of the prism.
First, let's find the area of the triangular base.
Given dimensions:
Base (b) = 10 inches
Height (h) = 8 inches
Area of a triangle = 1/2 * base * height
Area = 1/2 * 10 * 8
Area = 40 square inches
Now, we need to find the volume of the triangular prism. The formula for the volume of a prism is:
Volume = base area * height
Substitute the values we found:
Volume = 40 * 12
Volume = 480 cubic inches
Therefore, the volume of the triangular prism shelf is 480 cubic inches.