Video: Finding the Volume of a Three-Dimensional Composite Figure in a Real-World Context

Benjamin made a cardboard house at school. The lower part of the house is a rectangular prism and the upper part a triangular prism. Find the volume of the house.

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Video Transcript

Benjamin made a cardboard house at school. The lower part of the house is a rectangular prism and the upper part a triangular prism. Find the volume of the house.

So we’re told the lower part is a rectangular prism and the upper part is a triangular prism. The volume of any prism is equal to the area of the base times the height of the prism. And it’s good to know that the height of the prism is the distance that connects the two bases. So the volume of the house will be found by finding the volume of the rectangular prism and adding the volume of the triangular prism together. And again that will give us the volume of the whole house.

So for the volume of the rectangular prism, we need to first find the area of the base. And with a rectangular prism, we can pick whichever two parallel faces we would like to be the bases. Let’s pick these two. So the area of the base will be length times width — so 17 times 20. And then the height of that prism is the distance between those bases and that will be 45. After multiplying these together, we would get 15300 cubic centimetres.

Now, let’s find the volume of the triangular prism. In order to find the area of the base, we need to find the area of the triangle, which is one-half times the base of the triangle times the height of the triangle. And then, we’ll multiply by the height of the prism.

So the base of the triangle will be 45 centimetres and then the height would be 18 centimetres. So now, we need the height of the prism. Here is our other base. Therefore, the distance between these triangles will be 17 centimetres.

So now, we need to multiply and we get 6885 cubic centimetres. So the volume of the house will be found by adding the volume of the rectangular prism and the volume of the triangular prism together to get 22185 cubic centimetres.

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