Question

A square PQRS of side 22 cm is divided into five equal parts. The central part is circular and the lines, PA, QB, RC and SD lie along the digonals PR and QS of the square.

Find
(i) The circumference of the central part.
(ii) The perimeter of the part PADS.

Answer 1

Side of square = 22cm
$\therefore Ar=22\times 22=484c{m}^2$
$\therefore$ Area of circle = $\frac{1}{5}\times 484$
$=\frac{1}{5}\times 484$
$r^2=\frac{1}{5}\times 484\times \frac{7}{44}$
$r^2=\frac{22\times 7}{5}$
$r=\sqrt{\frac{22\times 7}{5}}=\sqrt{\frac{154}{5}}=5.5cm$
Thus circumference = $2\pi r=2\times \pi \times T.T$
Perimeter of PADS = PS+2(PA)+AD
$=PS+2[\frac{1}{2}PR-r]+\frac{1}{4}\times 2\pi r$