In the adjoining figure, the point D divides the side BC of ∆ABC in the ratio m:n. Prove that ar(∆ABD): ar(∆ADC) = m:n.

Given: D divides the side BC of ∆ABC in the ratio m:n

Area (Δ ABD) = 1/2 × BD × AL

Area (Δ ADC) = 1/2 × CD × AL

Area (∆ABD): Area (∆ADC) = 1/2 × BD × AL: 1/2 × CD × AL

Area (∆ABD): Area (∆ADC) = BD: CD

Area (∆ABD): Area (∆ADC) = m: n (∵ BD:CD = m:n)