| In the given figure, the side of square ABCD is 7 cm. What is the area of the shaded portion formed by the arcs BD of the circles with the centre as C and A? |
 |
A) \[7\,\,c{{m}^{2}}\]
B) \[28\,\,c{{m}^{2}}\]
C) \[14\,\,c{{m}^{2}}\]
D) \[21\,\,c{{m}^{2}}\]
Correct Answer: B
Solution :
(b)| We have, two sectors BCD and ABD. |
| Both are symmetrical. |
| Area of shaded portion = Area of sector BCD\[-\]Area of \[\Delta BCD\] |
| \[=\frac{\pi {{r}^{2}}\theta }{360{}^\circ }-\frac{1}{2}\times b\times h\] |
| \[=\frac{\pi \,\,{{(7)}^{2}}\times 90{}^\circ }{360{}^\circ }-\frac{1}{2}\times 7\times 7\] |
| \[=\frac{77}{2}-\frac{49}{2}=28/2\,\,sq\,\,cm\] |
| \[\therefore \]Area of complete shaded region |
| \[=2\times \frac{28}{2}=28\,\,c{{m}^{2}}\] |
You need to login to perform this action.
You will be redirected in
3 sec
