+895 In trapezoid EFGH, \overline{EF} \parallel \overline{GH}, and P is the point on \overline{EH} such that EP:PH = 1:2. If the area of triangle PEF is 6, and the area of triangle PGH is 6, then find the area of trapezoid EFGH.
+15000 Find the area of trapezoid EFGH.
The height of the trapezoid EFGH is h.
\(A_{EFP}=\frac{\overline{EF}}{2} \cdot \frac{h}{3}=6\\ \overline{EF}=\frac{36}{h}\\ A_{GHP}=\frac{\overline{GH}}{2} \cdot \frac{2h}{3}=6\\ \overline{GH}=\frac{18}{h}\)
\(A_{EFGH}=\frac{\frac{36}{h}+\frac{18}{h}}{2}\cdot h\\ \color{blue}A_{EFGH}=27\)
The area of trapezoid EFGH is 27.
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