$M$ is the midpoint of the side $A B$ of a parallelogram $A B C D .$ If $a r (A M C D) = 24 {c m}^{2},$ find $a r (Δ A B C) .$

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Solution

$\begin{matrix} W e h a v e a r (A M C D) = a r (A C D) + a r (A M C) a r (A C D) = a r (A B C) = \frac{1}{2} a r (A B C D) a r (A M C) = \frac{1}{2} a r (A B C) = \frac{1}{4} a r (A B C D) n o w, 24 = \frac{1}{2} + \frac{1}{4} a r e a (A B C D) 24 = \frac{3}{4} a r (A B C D) 32 = a r (A B C D) ∴ a r (A B C) = 16 c m^{2} \end{matrix}$

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