Question

Find the perimeter of the given figure which involves four semicircles each drawn on side of a square of side 14 cm.

Answer 1

$\text{\underline{\underline{Answer :}}}$

$\bold{144 \ cm}$



$\text{\underline{\underline{Explaination :}}}$

$\sf{For \ diagram, \ refer \ to \ Attachment.}$

$\sf{Side \ of \ square = 14 \ cm}$

${\boxed{\sf{Perimeter = 4 ( Side )}}}$

$\sf{Perimeter = 4 ( 14 ) = 56 cm}$

$\sf{Now,}$

$\sf{\underline{Side \ of \ square = Diameter \ of \ circle}}$

$\therefore$

$\sf{Diameter \ of \ circle = 14 \ cm}$

$\sf{Radius \ of \ circle = {\dfrac{Diameter}{2}}}$

$\sf{Radius = {\dfrac{14}{2}} = 7 cm}$

${\boxed{\sf{Circumference \ of \ semi-circle = \pi r}}}$

$\sf{Circumference = {\dfrac{22}{7}} × 7}$

$\sf{Circumference = 22 \ cm}$

$\sf{Circumference \ of \ 4 \ semi-circles = 4 (22)}$

$\sf{Circumference = 88 \ cm}$

$\sf{Perimeter \ of \ figure = Sum \ of \ all \ sides}$

$\sf{Perimeter = 56 + 88 = 144 \ cm}$