question_answer

       All the vertices of a rhombus Lie on a circle. Find the area of the rhombus, if area of the circle is\[706.5c{{m}^{2}}\].(Take \[\pi =3.14\])

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 \[ABCD=\frac{1}{2}(AC\times BD)\]

\[=\frac{1}{2}(2r\times 2r)=2{{r}^{2}}\]

\[=(2\times 225)c{{m}^{2}}=450c{{m}^{2}}\]