¶ 2022 AMC8 Problem 24
Problem:
The figure below shows a polygon , consisting of rectangles and right triangles. When cut out and folded on the dotted lines, the polygon forms a triangular prism. Suppose that and . What is the volume of the prism?
Answer Choices:
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Solution:
When folded, point coincides with , point with , point with , and point with . The triangular prism can be oriented to have as the base and as the height. Note that , so is a right triangle with legs of lengths and , and an area of . The volume of a prism is the area of its base multiplied by its height, and so the volume is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions