Question

Find the perimeter of the shaded portion$\left(PQRSTUVW\right)$

• A. $104.56cm$
• B. $98cm$
• C. $112.56cm$
• D. $92.56cm$

Answer 1

The correct option is A $104.56cm$

Perimeter of the rectangle $ABCD=2(l+b)=2\times (26+28)=2\times 54=108$

perimeter of the Arc$=r\times \theta$

Here,$radius\left(r\right)=2cm,centralangle\left(\theta \right)=\frac{\pi }{2}$

perimeter of the Arc$=2\times \frac{\pi }{2}=\pi$

$perimeter=P\left(ABCD\right)+4\left(perimeterofArc\right)-8\left(radiusofthearc\right)$ (minus ${}^{\prime }{16}^{\prime }\because$ deduct ${}^{\prime }{8}^{\prime }$ times period of DU of along each corners.)

$=108+4\left(\pi \right)-(8\times 2)$

$=108+4\left(3.14\right)-16$

$=108+12.56-16$

$=104.56cm$

$\therefore$ the perimeter of the shaded region is $104.56cm$