question_answer

Find the area of the shaded region in the given figure of square ABCD.

A) \[100\,\,c{{m}^{2}}\]                      

B)  \[50\,\,c{{m}^{2}}\]

C)  \[60\,\,c{{m}^{2}}\]                       

D)  \[120\,\,c{{m}^{2}}\]

Correct Answer: B

Solution :

Area of shaded region = Area of square - Area of \[\left[ \Delta DEG+\Delta EAF+\Delta CFB \right]\] \[={{10}^{2}}-\left[ \frac{1}{2}\times 4\times 5+\frac{1}{2}\times 5\times 4+\frac{1}{2}\times 6\times 10 \right]\] \[=100-\left[ 10+10+30 \right]=100-50=50\,\,c{{m}^{2}}\]