Question

Dreptunghiul ABCD are aria egala cu 40. M si N sunt mijloacele laturilor[BC], respectiv [CD]. Aflati aria triunghiului AMN? Va rog este urgent!! Dau coroana;)!!

Answer 1

[tex]A_{\Delta AMN}=A_{ABCD}-A_{\Delta ADN}-A_{\Delta NCM}-A_{\Delta ABM}\\ A_{\Delta AMN}=A_{ABCD}-\dfrac{AD\cdot DN}{2}-\dfrac{AB\cdot BM}{2}-\dfrac{NC\cdot MC}{2}\\ A_{\Delta AMN}=A_{ABCD}-\dfrac{AD\cdot DC}{4}-\dfrac{AB\cdot BC}{4}-\dfrac{BC\cdot CD}{8}\\ A_{\Delta AMN}=A_{ABCD}-\dfrac{A_{ABCD}}{4}-\dfrac{A_{ABCD}}{4}-\dfrac{A_{ABCD}}{8}\\ A_{\Delta AMN}=\dfrac{3}{8}\cdot A_{ABCD}=\boxed{15\ cm^2}[/tex]