Question

All the vertices of a rhombus lie on a circle., if area of the circle is 1256 $c{m}^2.$ (Use $\pi =$ 3.14), then find out the area of the rhombus?

• A. $1600c{m}^2$
• B. $800c{m}^2$
• C. $400c{m}^2$
• D. $200c{m}^2$

Answer 1

The correct option is B $800c{m}^2$

$Given-ABCDisarhombusinscribedinacirclewithcentreO.ar.circle=A=1256{cm}^2.Tofindout-ar.ABCD=?Solution-Letthediameterofthecirclebed.Thend=\sqrt{\frac{4A}{\pi }}=\sqrt{\frac{4\times 1256}{3.14}}cm=40cm.Nowthediagonalsoftherhombus=a=diameterdofthecirclesincetherhombusisinscribedinthecircle.Obviously,boththediagonalsareequal.\therefore ar.ABCD=\frac{1}{2}\times a\times a=\frac{1}{2}\times 40\times 40{cm}^2=800{cm}^2.Ans-OptionB.$