Question

In the given figure, E is any point on median AD of a ΔABC. What is ar (ABE) ?

• A. ar (DCE)
• B. ar (ABE)
• C. ar (ACE)
• D. ar (EBC)

Answer 1

The correct option is C

ar (ACE)

AD is the median of △ABC. Therefore, it will divide △ABC into two triangles of equal areas.

Therefore, Area (△ABD) = Area (△ACD) ... (1)

ED is the median of △EBC.

Therefore, Area (△EBD) = Area (△ECD) ... (2)

On subtracting equation (2) from equation (1), we obtain

Area (△ABD) − Area (△EBD) = Area (△ACD) − Area (△ECD)

Area (△ABE) = Area (△ACE)