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A trapezoid $ABGE$ is partitioned into three smaller shapes: a trapezoid $ABCD$, a parallelogram $CDEF$, and a triangle $CFG$. The sides $AB || CD$, and $2AB = CD$. The number in each colored region indicates the area of each shape.

What is the area of the blue parallelogram?

 

 Jan 24, 2021
 #1
avatar+112523 
+1

The question basically states that the answer will be the same no matter what trapezium (trapezoid in your country) you use so long as it fits the description.

So I took the liberty of making angle AEG a right angle.

 

Here is the pic I used

 

 

I worked out that k=3/2  and then you can work out the blue area.

 Jan 24, 2021
 #2
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Angle AEG = 90 deg.          angle BGE = 45 deg.

 

[CDEF] = 8 square units

 Jan 24, 2021
edited by Guest  Jan 24, 2021
 #3
avatar+112523 
+1

Where do you get 45 degrees from?

Melody  Jan 24, 2021
 #4
avatar+1032 
+2

AB = AD = 1.632993161

DC = EF = 2*AB = 3.265986322

DE = CF = FG = 2.449489743

[CDEF] = 3.265986322 * 2.449489743 = 8

Diagram not to scale

jugoslav  Jan 25, 2021
 #5
avatar+112523 
+1

Where do all your added numbers come from?

I know what the answer is. I answered first.

But neither of you 2 has said where any of your numbers come from.

 

Oh I get it.

You both arbitrarily chose angle AEG to be 90 degrees  AND angle EGB=45 degrees.

And you arbitrarily chose AB to equal AD

Only you didn't bother to explain that is what you were doing.

 

This does make it easier,

You do not need to approximate anything though.

 

If you let AB=x units and  CF=h units  then 

it is easy to work out that h=sqrt6,   and x=sqrt(8/3)

And then that blue area = 8 units squared.

Melody  Jan 25, 2021

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