# Thread: Find the Area of a Portion of a Square

1. ## Find the Area of a Portion of a Square

Dear Sir,
I appreaciate very much if someone can help me in the below question.
Thanks

ABCD is a square. AFC and BFE are straight lines. Given AE = ED. Find the shaded area of the square.

2. ## re: Find the Area of a Portion of a Square

EBA is 0.25 ABCD and ABC is 0.5 ABCD does that help?

3. ## re: Find the Area of a Portion of a Square

To use reply #2, you must know that triangles $\Delta EFA~\&~\Delta CFB$ are similar.
So the area of $\Delta EFA$ is one-forth the area of $\Delta CFB$

4. ## re: Find the Area of a Portion of a Square

I am aware that fact and also ABC is 0.5 of ABCD but got stuck from here on.

5. ## re: Find the Area of a Portion of a Square

Yes I know it can be done using Similar Traingles facts but I wonder how it can be done by a simpler approach. This is what required in this question for students who have not studied similar triangles.
thanks

6. ## re: Find the Area of a Portion of a Square

Hi kingman,
Draw a line fromE parallel to AB meeting AC @ G. The area you seek consists of one squareand 1/2 square side lengths a/2 plus triangle EFG where a is length of large square side.Your problem is then to find the altitude of EFG