Sometimes you have to find the volume of a shape that is composed of two or more rectangular prisms. These are called composite prisms. Click on the slide show below to see how you can find the volume of one of these shapes.
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Take a look at this shape.
At first glance, this may not look like a rectangular prism. The base of this prism certainly doesn't look like a rectangle.
But take a closer look. You can actually break this base up into three rectangles.
This means you can break this strange-looking prism into three rectangular prisms.
If you find the area of this base. . .
. . . then you can find the volume of this prism.
Remember the volume can be found by taking the area of the base (l × w) and multiplying it by the height (h). What's the area of the biggest rectangle?
The biggest rectangle has dimensions 2 x 8, so the area is 16 square units. Now let's find the area of the middle rectangle. We see that the side length is 2 units. But how long is it? With a little bit of detective work, we can see that the side length = 3 + 1 + 1 = 5 units.
So what is the area? The area of the middle rectangle is 2 units × 5 units = 10 square units. We have one more rectangle to find the area of—the tiny rectangle at the front. The area of this one is 3 units × 1 unit = 3 square units.
Now we add up the 3 smaller areas to get the area of the entire base. So 16 square units + 10 square units + 3 square units = 29 square units. Now that we know the area of the base, we can find the volume of this prism. All we have to do is multiply the area of the base of the prism by the height. This prism is 4 units tall. Its base has an area of 29 square units.
V = Bh |
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