Question

M is the midpoint of side AB of a parallelogram ABCD.If ar(AMCD) =$24c{m}^2$,find ar($△ABC)$.

Answer 1

Join AC.
AC divides parallelogram ABCD into two congruent triangles of equal areas.
ar△ABC=ar△ACD=1/2arABCD
M is the midpoint of AB. So, CM is the median.
CM divides △ABC in two triangles with equal area.
ar△AMC=ar△BMC=1/2ar△ABC
ar(AMCD) = ar(△ACD) + ar(△AMC) = ar(△ABC) + ar(△AMC) = ​ ar(△ABC) + 1/2​ ar(△ABC)
⇒24=3/2ar△ABC⇒ar△ABC=$16c{m}^2$