In the figure, ABCD is a rectangle. CDE is a straight line and AE//BD. If the area of ABCD is 24 and F is a point on BC such that BF:FC=3:1, find the area of triangle DEF.
@Callisto @hartnn

Question

In the figure, ABCD is a rectangle. CDE is a straight line and AE//BD. If the area of ABCD is 24 and F is a point on BC such that BF:FC=3:1, find the area of triangle DEF.
@Callisto @hartnn

anonymous · Answer

|dw:1418132482073:dw|

callisto · Answer

Let BC = l, DC = w
Given lw = 24, and BF:FC = 3:1 => BF = 3l/4 , FC = l/4
DE = AB = DC = w
Area of DCF = DC * FC / 2 = (lw/4) / 2 = lw/8
Area of ECF = EC * FC / 2 = (2lw/4) / 2 = lw/4

Area of DEF = Area of ECF - Area of DCF = lw /4 - lw/8 = ...
And you know what lw is from the beginning

anonymous · Answer

:O ....
amazing!

hartnn · Answer

as always

callisto · Answer

You got it?!!

anonymous · Answer

Callisto you are my goddess <3
i also think of the triangles EFC and DFC at the beginning but i don't know how to do next lol. got it and thank you so muchhhhhhhhhh

hartnn · Answer

DE = AB
was that given ? or found ?

anonymous · Answer

parallel

callisto · Answer

DE=AB because it's a parallelogram LOL

anonymous · Answer

AE//BD, then AB=ED

callisto · Answer

ABDE is a parallelogram*

hartnn · Answer

got it

hartnn · Answer

how do you even ... ?
have you solved them before ?

hartnn · Answer

was asking calli....how could these ideas come to her so fast!

callisto · Answer

The secret has been told in this guy's profile :P

callisto · Answer

http://openstudy.com/users/hartnn

anonymous · Answer

1) Practice, 
2) More Practice,
3) More and more practice.

anonymous · Answer

Need to know 4th ? ;)

XD

hartnn · Answer

lol, i had to look at my profile for the secret :P

callisto · Answer

You need not, 'cause you wrote it :P

hartnn · Answer

i never read the link before opening it :P