Question Number 208943 by MWSuSon last updated on 28/Jun/24
Answered by A5T last updated on 28/Jun/24
![a. (([ADM])/([ABCD]))=(((1/2)×AD×DM)/(AD×(DM×2)))=(1/4) b. Let AM and DN intersect at E (([DEM])/([ABCD]))=(((1/2)×((AD)/2)×DM)/(AD×DM×2))=(1/8) c. 1−(1/4)−(1/8)=(5/8)](https://www.tinkutara.com/question/Q208944.png)
$${a}.\:\frac{\left[{ADM}\right]}{\left[{ABCD}\right]}=\frac{\frac{\mathrm{1}}{\mathrm{2}}×{AD}×{DM}}{{AD}×\left({DM}×\mathrm{2}\right)}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${b}.\:{Let}\:{AM}\:{and}\:{DN}\:{intersect}\:{at}\:{E} \\ $$$$\frac{\left[{DEM}\right]}{\left[{ABCD}\right]}=\frac{\frac{\mathrm{1}}{\mathrm{2}}×\frac{{AD}}{\mathrm{2}}×{DM}}{{AD}×{DM}×\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$$${c}.\:\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{8}}=\frac{\mathrm{5}}{\mathrm{8}} \\ $$