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trapezoid - Puerto Rico TST 2022.1.5

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March 23, 2024
geometrytrapezoid

Problem Statement

Let ABCDABCD be a trapezoid of bases ABAB and CDCD, and non-parallel sides BCBC and DADA. The angles ∠BCD\angle BCD and ∠CDA\angle CDA are acute. The lines BCBC and DADA are cut at a point EE. It is known that AE=2AE = 2, AC=6AC = 6, CD=72CD =\sqrt{72} and area (△BCD)=18( \vartriangle BCD)= 18. (a) Find the height of the trapezoid ABCDABCD. (b) Find the area of △ABC\vartriangle ABC.
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