Question

In the given figure, BC ∥ DE.
(a) If area of ΔADC is 20 sq. units, find the area of ΔAEB.
(b) If the area of ΔBFD is 8 square units, find the area of ΔCEF

Answer 1

(a) Triangles on the same base and between the same parallels are equal in area.
∴ A(ΔDBC) = A9ΔECB)     ....(i)
Now,
A(ΔABC) = A(ΔADC) + A(ΔDBC) = A(ΔAEB) + A(ΔECB)
⇒ A(ΔAC) + A(DBC) = A(ΔAEB) + A(ΔECB)
⇒ A(ΔADC) = A(ΔAEB)   ....(ii)   [from (i)]
Given, A(ΔADC) = 20 sq. units
⇒ A(ΔAEB) = 20 sq. units

(b) A(ΔADC) = A(ΔAEB)  ...[From (ii)]
⇒ A(ΔADC) - A(ΔDEF) = A(ΔAEB) - A(ΔDFE)
⇒ A(ΔCEF) = A(ΔBFD)
Given, A(ΔBFD) = 8 sq. units
⇒ A(ΔCEF) = 8 sq. units.