In this explainer, we will learn how to find volumes of composite solids consisting of two or more regular solids.

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### Definition: Composite Solid

A composite solid is a solid made of two or more well-defined solid objects.

In order to find the volume of a composite solid, one needs to identify the different parts it is made of. This decomposition allows working out the volume of each part independently. The volume of the composite solid is simply the sum of the volumes of its parts. For composite prisms, where the bases are a composite shape, the area of the bases is the sum of the areas of the parts it is made of. The volume of the composite prism is then given by multiplying the whole base area by the height of the prism.

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Let’s work out some examples.

### Example 1: Finding the Volume of a Composite Prism

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

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### Answer

This cardboard house is a composite prism: it has two parallel congruent shapes (the bases) and its cross-section is constant. The shape of its base is composite: it is made of a rectangle and a triangle.

To find the volume of this cardboard house, we need to find the areas of the rectangle