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:
Since maps to on the map, we know . Since is a rectangle with and being opposite, we know . Since maps to on the map, we know . Since is a rectangle with and being opposite, we know . Since is a rectangle with and being opposite, we know . Since , we know . The area of is . Now, we can make this prism complete with bases of and . The volume of a prism is the area of the base times the altitude to the base. We can use as our base and as our altitude. This would make our volume equal to
Thus, the answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions