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Omni-MATH / Let AD,BE, and CF be segments sharing a common midpoint, with AB<AE and BC<BF. Suppose that each pair of segments forms a 60^(∘) angle, and that AD=7,BE=10, and CF=18. Let K denote…

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problem

Let AD,BEAD, BE, and CFCF be segments sharing a common midpoint, with AB<AEAB < AE and BC<BFBC < BF. Suppose that each pair of segments forms a 60∘60^{\circ} angle, and that AD=7,BE=10AD=7, BE=10, and CF=18CF=18. Let KK denote the sum of the areas of the six triangles △ABC,△BCD,△CDE,△DEF,△EFA\triangle ABC, \triangle BCD, \triangle CDE, \triangle DEF, \triangle EFA, and △FAB\triangle FAB. Compute K3K \sqrt{3}.
Plain-text mathematical notation (without MathML)
Let AD,BE, and CF be segments sharing a common midpoint, with AB<AE and BC<BF. Suppose that each pair of segments forms a 60^(∘) angle, and that AD=7,BE=10, and CF=18. Let K denote the sum of the areas of the six triangles △ABC,△BCD,△CDE,△DEF,△EFA, and △FAB. Compute K√(3).
Original LaTeX notation
Let $AD, BE$, and $CF$ be segments sharing a common midpoint, with $AB < AE$ and $BC < BF$. Suppose that each pair of segments forms a $60^{\circ}$ angle, and that $AD=7, BE=10$, and $CF=18$. Let $K$ denote the sum of the areas of the six triangles $\triangle ABC, \triangle BCD, \triangle CDE, \triangle DEF, \triangle EFA$, and $\triangle FAB$. Compute $K \sqrt{3}$.

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task_id
fecc7c1a-5973-5e6a-9c3d-040b9a7562d7
task_key
test--fecc7c1a-5973-5e6a-9c3d-040b9a7562d7
task_revision_id
1
config / split
/ test

Official source

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