ABCD is a rectangle and BD is one of its diagonals. If ar(Δ ABD) = 8 cm² . Find ar(ΔBCD).

In the above figure, we have two right-angled triangles ΔABD and ΔBCD.

Now in ΔABD and ΔBCD

AB = DC (∵ opposite sides of rectangle are equal)

∠BAD = ∠BCD (∵ both are 90°)

AD = BC (∵ opposite sides of rectangle are equal)

∴ ΔABD ≅ ΔBCD(SAS property)

As congruent triangles have equal area.

∴ ar(ΔABD) = ar(ΔBCD)

∴ Area of ΔBCD = 8cm²