Determine the volume of the given triangular prism.
The volume of a triangular prism can be found by multiplying the base times the height, where the shaded pink portion represents the base. The volume is then the area of the base multiplied by the height. And the green portion represents the height. It’s the distance from one base to the other.
And how do we go about finding the area of the base? Well, like any triangle, we multiply one-half, the base of that triangle, times the height of that triangle. So we see, in our case, the base of our triangle is 10 feet and the height of our triangle is six feet. And the height of our triangular prism is 17 feet.
Let’s start plugging things into our formula. For our base, our triangle, one-half times six times 10. Then we multiply the area of our base by the height of our prism, 17 feet. Now we simply multiply. six times 10 times one-half equals 30. And 30 times 17 equals 510.
But we’re not finished here because we need to decide what to do with our units. When we multiply feet by feet by feet and when we’re discussing volume, we know that our units will be cubed. That’s our final answer: The volume of the given triangular prism equals 510 feet cubed.