https://postimg.org/image/uqjte5eg3/
ABCD is a quadrilateral.
AE=EB and DF=FC
AF intersection DE={K}
BF intersection CE={P]
AREA AKD=M
AREA PBC=Y
Find area of EPFK?

I am sure the answer is M+Y but I can't find a way.

2. ## Re: quadrilateral

EPFK = ABCD - ADE - DFK - BCE - CFP

Silly problem...

3. ## Re: quadrilateral

Originally Posted by DenisB
EPFK = ABCD - ADE - DFK - BCE - CFP
Silly problem...
And even a sillier reply with totally meaningless notation.

4. ## Re: quadrilateral

Agree...thanks Plato, that's what I was trying for!

5. ## Re: quadrilateral

Is the question wrong?

6. ## Re: quadrilateral

Don't ask Plato: he's in a grouchy mood !!

7. ## Re: quadrilateral

Is it wrong or something missing?

8. ## Re: quadrilateral

Originally Posted by kastamonu
Is it wrong or something missing?
After looking at the diagram, and looking at what the givens are intended for the diagram, I would state the problem as follows,
excepting that someone else might use more compact notation:

ABCD is a quadrilateral.

Line segment AE is congruent to line segment EB.
Line segment DF is congruent to line segment FC.
Line segment AF intersects line segment DE at point K.
Line segment BF intersects line segment CE at point P.

The area of triangle AKD = M.
The area of triangle PBC = Y.

Find the area of quadrilateral EPFK in terms of M and Y.

(Note: The diagram is not drawn to scale.)

9. ## Re: quadrilateral

There is no ratio to find the areas.I think the question is wwrong.

10. ## Re: quadrilateral

Originally Posted by greg1313
(Note: The diagram is not drawn to scale.)
What else is new?
Do you think AD is parallel to BC?

11. ## Re: quadrilateral

Originally Posted by kastamonu
There is no ratio to find the areas.
I think the question is wrong.
Why then did you bravingly say:
"I am sure the answer is M+Y" ?

12. ## Re: quadrilateral

Because according to the book this is the answer. What can I do other than to trust the book?

13. ## Re: quadrilateral

Terrific answer...I should have thought of that...

14. ## Re: quadrilateral

I talked with the author. He is checking.

15. ## Re: quadrilateral

|AEK| + M + |FPC| + Y = |AED| + |FBC|
= |EBD| + |DBC|
= |EBFD|
= |EBF| + |DEF|
= |AEF| + |FEC|
= |AEK| + |FPC| + |EPFK|

So |EPFK| = M + Y

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