## Tomas.A 3 years ago Triangle, AC=20, AD=18, CE=24, AE=EB, BD=DC picture below. Find area of triangle.

1. Tomas.A

2. King

25sqrt3?

3. Tomas.A

i don't know

4. Mertsj

|dw:1327412914643:dw|

Is this a right triangle (<ACB =90 degrees?)

6. Tomas.A

i don't know, it may be, just prove it :D

EC=24 (given) Where does the "8" fit in??

@Mersj, does the 8 in your drawing apply to EC?

9. Tomas.A

i don't know how to explain in english but he's right :D but i don't know where he got 96

10. Tomas.A

EF=8 not EC

11. Mertsj

A median divides a triangle into 2 triangles of equal area. A second median divides the triangles form by the first median into triangles whose areas are in the ratio 2:1. We can find the area of triangle ACF using Heron's formula. It is 96. So triangle CFD is 48. Together they make triangle ACD which is half the area of the entire triangle. 48+96=144 and 144 times 2 = 288 and that is the area of triangle ABC

12. Mertsj

No. The 8 is EF

13. Mertsj

Remember the intersection of medians divides the medians into 1/3 2/3 segments

Very good Mertsj, thanks for the explanation.

15. Mertsj

yw

16. Tomas.A

ok i knew that each median divides by 1:2 but never knew that it also divides area

17. Mertsj

Yes. And if you drew the third median, you would have 6 triangles of equal area.