M is the midpoint of the side AB of a parallelogram ABCD. If ar(AMCD) = 24 cm², find ar(∆ABC).

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Solution

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

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M is the midpoint of the side AB of a parallelogram ABCD. If ar(AMCD) = 24 cm2, find ar(∆ABC).

M is the midpoint of the side AB of a parallelogram ABCD. If ar(AMCD) = 24 cm², find ar(∆ABC).