The skill being taught is using the Pythagorean theorem in three dimensions to find the diagonal distance inside a rectangular prism to a specific endpoint. The process involves calculating distances along multiple right triangles formed within the prism.
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Pythagoras in 3D with a rectangular prism
Test your understanding of Pythagoras in 3D with a rectangular prism by practicing it! Work through the below exercises to use it in practice.
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Let's use Pythagoras to solve for the distance across this rectangular prism to the top mid-point.
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First we can find the distance to the midpoint of the line on the bottom. Notice that it's only a distance of 4 on the second leg of the right triangle.
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Now we have another right triangle with legs of root 32 and 7, where the hypotenuse forms the distance we are looking to solve for.
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Root 32, squared, is just 32, so we have the root of 32 plus 49
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Which is root 81, or just a distance of 9