Question

An NGO has decided to start a campaign about the consumer services, to spread awareness about the consumer courts and their benefits. For the same purpose, it makes some badges in the shape as shown in the figure, such that AB=BC=CD=DE =21 cm. Find the area and perimeter of the badge (shaded region.)

Answer 1

Here we can see that AGBHCFA and EJCIDKE are exactly same so we will f area of one region and double it to get the overall area  

Now the area of semicircle  AFC 

=  $\frac{ \pi r^{2}}{2} = \frac{ \pi * 21^{2} }{2} = \frac{441}{2} \pi cm^{2}$

 

Area of semicircle AGB 

=  $\frac{ \pi r^{2}}{2} = \pi * (21/2 )^{2} / 2 = 441/8 \pi c m^{2}$

 

And area of semicircle BHC 

= $\frac{ \pi r^{2}}{2} = \pi * (21/2 )^{2} / 2 = 441/8 \pi c m^{2}$

 

So area of shaded portion AGBHCFA 

= $441/2 \pi - 441/8 \pi + 441/8 \pi$

=  $441/2 \pi c m^{2} [tex]</p><p> </p><p>So area of the shaded portion AGBHCJEKDICFA </p><p>=  [tex]2 * 441/2 \pi c m^{2} = 441 \pi c m^{2}$