Question

In Fig. 7, OABC is a rectangle inscribed in a quadrant of a circle of radius 25 cm. Find the area of the rectangle, if OC = 7 cm.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{OC}=7\mathrm{cm}\mathrm{and}\mathrm{radius},\mathrm{OB}=25\mathrm{cm} \\ \mathrm{In}∆\mathrm{OBC},\mathrm{using}\mathrm{pythagoras}\mathrm{theorem},\mathrm{we}\mathrm{get} \\ \mathrm{BC}=\sqrt{{\mathrm{OB}}^2-{\mathrm{OC}}^2} \\ =\sqrt{{25}^2-7^2} \\ =\sqrt{625-49} \\ =\sqrt{576} \\ =24\mathrm{cm} \\ \mathrm{Now},\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{rectangle}\mathrm{OABC}=\mathrm{OC}\times \mathrm{BC} \\ =7\times 24 \\ =168{\mathrm{cm}}^2 \end{gathered}$$

So, the area of the rectangle is 168 cm².