Question

find the perimeter of the following shapes to one decimal place .(Take

$\pi = 3.14$
​

Answer 1

Answer:

$\mathrm{28.8\:cm}$

Step-by-step explanation:

First of all, we need to figure out what all does the shape consists of.

We can say that the figure consists of 2 half circles without the diameter ( One with diameter 8 cm and other with diameter 4 cm), and 3 lines ( 2 lines 3 cm each and 1 line 4 cm).

Let's start solve this question!!

$\mathrm{Perimeter\:of\:semicircle\:=\:\dfrac{1}{2} \cdot \pi \cdot d}$

$\textrm{Perimeter of the semicircle with diameter 8 cm = }\dfrac{1}{2}\cdot\pi\cdot 8 = \pi \times 4 = 12.56$

$\textrm{Perimeter of the semicircle with diameter 4 cm = }\dfrac{1}{2}\cdot\pi\cdot 4 = \pi \times 2 = 6.28$

We calculated all the necessary values.

Let's add them.

Perimeter of the shape = Perimeter of both the semicircles + Those 3 lines.

$\implies \textrm{Perimeter of the shape = }12.56 + 6.28 + 4 + 3 + 3 = \underline{\underline{28.84 \textrm{ cm}}}$

The question also says in one decimal place, so Perimeter = 28.8 cm

Answer 2

Solution

Big Semicircle

From the figure,

It is apparent the diameter of the semicircle is 8 cm

Radius would be 4 cm

Perimeter of SemiCircle would be :

$\large{ \tt{\pi \: r}} \\ \\ \hookrightarrow \: \boxed{ \tt{a = 4\pi \: cm}}$

Three Lines

$\tt{b = 4 + 2(3) = 10 cm}$

Smaller SemiCircle

The radius would be 2 cm

$\hookrightarrow \: \sf{c = 2\pi \: cm}$

Perimeter of the whole figure

$\tt{a + b + c} \\ \\ = \tt{6\pi \: + 22} \\ \\ = \tt{18.8 + 10} \\ \\ = \large{\tt{28.8 \: cm}}$

The perimeter of the whole figure is 28.8 cm