# Find the Area of a Portion of a Square

• September 3rd 2011, 02:14 PM
kingman
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.
• September 3rd 2011, 02:24 PM
pickslides
re: Find the Area of a Portion of a Square
EBA is 0.25 ABCD and ABC is 0.5 ABCD does that help?
• September 3rd 2011, 03:35 PM
Plato
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 $\Delta CFB$
• September 3rd 2011, 04:08 PM
kingman
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.
• September 3rd 2011, 04:13 PM
kingman
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
• September 3rd 2011, 04:31 PM
bjhopper
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