Question 1189476
<pre>

Instead of doing it for you, I'll do one exactly like yours with 
different numbers, so you can follow it step by step:

In the diagram below, AEFD is a rectangle. G and H are midpoints of
Line EK and Line FK respectively, and K is the midpoint of Line AD. 
If the area of the indicated lower region is 51 cm^2, what is y, in 
cm?

{{{drawing(400,2000/11,-11,11,-1,9,

line(-10,0,10,0), line(-10,0,-10,34/5), line(-10,34/5,10,34/5),line(10,34/5,10,0),
line(-10,0,0, 34/5), line(10,0,0,34/5), locate(-10,0,E), locate(10,0,F),
locate(-10,7.7,A), locate(10,7.7,D), locate(0,7.7,K),
line(-5,17/5,5,17/5),locate(-5.7,4,G),locate(5.2,4,H),
locate(-4,2.5,matrix(1,5,THIS,AREA,""="",51,cm^2)),
locate(-1,0,matrix(1,2,20,cm)),locate(10.1,3.8,y)
 
)}}}

The figure GEFH is a trapezoid, and the area is given by the formula

    {{{A}}}{{{""=""}}}{{{expr(1/2)(b[1]+b[2])h}}}

GH is the midline of the triangle KEF, so it is half EF, 
or 10 cm., where the b's are the two parallel sides and 
h is the height, which is half of y.

    {{{51}}}{{{""=""}}}{{{expr(1/2)(10^""+20)(expr(1/2)y)}}}

Solve that and get {{{y = 34/5}}} cm. or {{{y=6&4/5}}}.

Edwin</pre>