Question

In the given figure, D is mid-point of side BC, the area of triangle BEA is equal to area of triangle:

Options

• BED

• CED

• CEA

• ACD

Answer 1

ACD

Explanation:

• Since D is the mid-point of side BC, the line segment AD is a median of ΔABC. A median divides a triangle into two triangles of equal area, meaning:
  area of ΔABD = area of ΔACD
• Similarly, in ΔEBC, D is the mid-point of BC, so ED is a median, which means:
  area of ΔEBD = area of ΔECD
• Subtracting the area of ΔEBD from the area of ΔABD:
  area of ΔBEA = area of ΔABD − area of ΔEBD
• Substituting ΔECD$ in place of ΔEBD (since their areas are equal):
  area of ΔBEA = area of ΔABD − area of ΔECD = area of ΔACD

Thus, the area of triangle BEA is equal to the area of triangle ACD.