Question

The circular portions of the following figures are
semicircles. For each of the following figures, fnd

its perimeter,

its area.
​

Answer 1

Answer:

i) 96cm

ii)661cm^2

Step-by-step explanation:

Ok, here mate.

i) Perimeter

First, let's divide the figure into 2 parts to make it easier:

a) Circle (formed by semi-circles)

b) Rectangle

a)Perimeter/Circumference of a circle, which is formed by 2 semicircles= 2*pi*r, where R is the radius, and pi is 22/7

How to find radius, knowing the diameter(21cm):

Radius=1/2 (Diameter)

Radius= 1/2 (21cm)

Radius=10.5cm

On calculating, you will get the answer: 66

Now for b:

b) Only the outer part of the rectangle would be needed, since it is the "perimeter" of the figure, so only the "width of the rectangle".

Let's see how to find the width now.

Width of rectangle = Total width of figure(36cm)-Width occupied by circle(10.5+10.5cm)

Width of rectangle= 36cm-21cm

//= 15cm

Since there are 2 widths= 15*2

//= 30cm

So now, the total perimeter:

c) 30cm(rectangle's part)+ 66cm(Semicircles' part)

It will give us 96cm

ii) Area:

For this, we have to find separately:

a) area of circle formed by semi-circles

b) area of the rectangle

a) Area= pi*r^2 (r represents radius, pi=22/7 or 3.14)

Area= 22/7*10.5^2

Area= 22/7*110.25cm^2

That will give us: 346.4cm^2

b) Rectangle's area= L*W

L= 21 cm

W (from before)= 15cm

Rectangle's area= 21cm*15cm

//= 315cm^2

Now for the final part, let's add the two up.

Total area= 315cm^2+346.4cm^2

That will give us: 661.4cm^2. On rounding the answer to 3 significant figures, it will give us 661cm^2.

Btw, I was just solving the question from my book, as homework. And... hope it helped. :)