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HELP GEOMETRY

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A regular tetrahedron has side length 1. A plane passing through four edge's midpoints cut the tetrahedron at the halfway as shown. Each piece has surface area expressed as $$\frac{m}{n}\sqrt{3} + \frac{p}{q}$$, where m,n as well as p,q are coprime positive integers. Find the value of m+n+p+q.

Jun 30, 2022