MO - triangles

On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB segments are divided into four parts. Find the areas of these four parts.

Correct result:

AED =  4 ha
ADF =  8 ha
BDE =  2 ha
BCFD =  13 ha

Solution:

AED=4 haAED=4 \ \text{ha}
ADF=8 haADF=8 \ \text{ha}
BDE=2 haBDE=2 \ \text{ha}
BCFD=13 haBCFD=13 \ \text{ha}



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