Question 1210497
.
In trapezoid EFGH, EF parallel GH, and P is the point on EH such that EP:PH = 1:1. 
If the area of triangle PEG is 4, and the area of triangle EFG is 4, then find the area of trapezoid EFGH.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



                This problem is easy.



<pre>
The area of trapezoid EFGH is the sum of areas of three triangles

    {{{area[EFGH]}}} = {{{area[EFG]}}} + {{{area[PEG]}}} + {{{area[PGH]}}}.


{{{area[EFG]}}} = 4  is given;

{{{area[PGE]}}} = 4  is given;

{{{area[PGH]}}} = {{{area[PGE]}}} = 4,  because triangles PGH and PGE have equal bases EP = PH
                                                                           and common altitude to their bases.


Therefore, {{{area[EFGH]}}} = 4 + 4 + 4 = 12 square units.    <U>ANSWER</U>
</pre>

Solved.