Geometry

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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