A) \[225\,c{{m}^{2}}\]
B) \[450\,c{{m}^{2}}\]
C) \[353\,c{{m}^{2}}\]
D) \[400\,c{{m}^{2}}\]
Correct Answer: B
Solution :
[b] Let ABCD be a rhombus whose vertices A 6, C, D lie on a circle with centre O and radius r. |
It is given that the area of the circle is \[706.5c{{m}^{2}}\]. |
\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\pi {{r}^{2}}=706.5\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3.14{{r}^{2}}=706.5\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{r}^{2}}=225\] |
We know that the diagonals of a rhombus bisect each other at right angle. Therefore, AC and BD are perpendicular and so these two are diameters of the circle. |
\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,AC=BD=2r\] |
Area of rhombus \[ABCD=\frac{1}{2}(AC\times BD)\] |
\[=\frac{1}{2}(2r\times 2r)=2{{r}^{2}}\] |
\[=(2\times 225)c{{m}^{2}}=450c{{m}^{2}}\] |
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