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Equilateral Hexagon Inside Triangle

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August 8, 2024
geometry2022

Problem Statement

In △PQR\triangle{PQR}, PQ=4PQ=4, PR=5PR=5, and QR=6QR=6. Assume that an equilateral hexagon ABCDEFABCDEF is able to be drawn inside △PQR\triangle{PQR} so that AB‾\overline{AB} is parallel to QR‾\overline{QR}, CD‾\overline{CD} is parallel to PQ‾\overline{PQ}, EF‾\overline{EF} is parallel to RP‾\overline{RP}, BC‾\overline{BC} lies on RP‾\overline{RP}, DE‾\overline{DE} lies on QR‾\overline{QR}, and AF‾\overline{AF} lies on PQ‾\overline{PQ}. Find the area of hexagon ABCDEFABCDEF.
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