# Working out the area of a triangle within another triangle [closed]

The area of $\triangle OBF$ is $5$ cm$^2$. $F$ is a point on $OA$ such that $OF = \dfrac9{11}OA$. Work out the area of $\triangle OBA$.

I have tried to solve this problem for a while, and just can't figure out how to do it. Please help.

Hint: Observe that both $\triangle OBF$ and $\triangle AOB$ have same height on bases $OF$ and $AO$

Here DE is perpendicular for $\triangle DCB$

• Why though? How would you define the height of the triangle on base OF or OA? I thought that the height was the length of the line drawn from the top vertex that makes a right angle with the base. With OF or OA as the base that doesn't seem possible.
– Ivan
May 31, 2018 at 16:51
• See OF and OA are common lines. i.e. OF lies on OA. So perpendicular from B to both OF and OA will be common May 31, 2018 at 16:52
• Still, I don't understand how that proves that the height remains the same.
– Ivan
May 31, 2018 at 16:54
• Do you know that perpendicular from a point to a line is always distinct? May 31, 2018 at 16:56
• You may draw the height of both triangles and see May 31, 2018 at 16:57