Question

In triangle ABC , O is the mid point of median AD prove that area of triangle OAB=1/4area of triangle ABC

Answer 1

Answer:

ANSWER

AD is the median of ΔABC.

Therefore, it will divide ΔABC into two triangles of equal area.

Area ΔABD = Area ΔACD

∴area(ΔABD)=

2

1

area(ΔABC) ------------(1)

In ΔABD, E is the mid-point of AD.

Therefore, BE is the median.

Then Area ΔBED = Area ΔABE

∴area(ΔABE)=

2

1

area(ΔABD) ------------(2)

area(ΔABE)=

2

1

×

2

1

area(ΔABC)

area(ΔABE)=

4

1

area(ΔABC)...........................(3)

In ΔADC, E is the mid-point of AD.

Therefore, EC is the median.

Area ΔAEC = Area ΔCED

∴area(ΔACE)=

2

1

area(ΔADC)

area(ΔACE)=

2

1

×

2

1

area(ΔABC)

area(ΔACE)=

4

1

area(ΔABC)....................(4)

From (3) and (4) we get

area(ΔABE)=area(ΔACE)

solution