Question

Im dreptunghiul ABCD consideram punctul M € CD astfel incat DM = 2MC. Stiind ca aria triunghiului BCM este de 12 cm², aflati aria patrulaterului ABMD. ajutor,dau coronita​

Answer 1

Explicație pas cu pas:

DM = 2MC => DC = 3MC

$\mathcal{A}_{\triangle BCM} = \dfrac{1}{3} \mathcal{A}_{\triangle BCD}$

$\implies \mathcal{A}_{\triangle BCD} = 3 \cdot 12 = 36 \ cm^{2}$

$\mathcal{A}_{\triangle BMD} = \dfrac{2}{3} \mathcal{A}_{\triangle BCD} = \dfrac{2}{3} \cdot 36 = 24 \ cm^{2}$

$\mathcal{A}_{\triangle ABD} = \mathcal{A}_{\triangle BCD} = 36 \ cm^{2}$

$\implies \mathcal{A}_{ABMD} = \mathcal{A}_{\triangle BMD} + \mathcal{A}_{\triangle ABD} \\ = 24 + 36 = \bf 60 \ cm^{2}$