Question 1189476: 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 shaded region is 45 cm^2, what is y, in cm?
Diagram: https://imgur.com/a/NJ9cV1f
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
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?
The figure GEFH is a trapezoid, and the area is given by the formula
  
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.
 
Solve that and get  cm. or  .
Edwin
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