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 Math Central Quandaries & Queries
 Question from Beth, a student: How do you find the height of the original square-based pyramid when given the sides (12cm) of the base and height (6cm) of the truncated pyramid, as well as the sides (3cm) of the base of the chopped off top (chopped off parallel to the base)?

Hi Beth,

I can get you started.

Imagine you have the original pyramid and you slice it with a plane which is perpendicular to the base, parallel to one side of the base and through the vertex $V.$ Here is my diagram of what you see.

Triangles $VAB$ and $VCD$ are similar.

Penny

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