Question

find the perimeter of the following shapes to 1 decimal place take pie = 3.14

Answer 1

Answer:

ii) Perimeter of the Shape = 53.69 m

iii) Perimeter of the shape = 88.24 cm

iv) Perimeter of the shape is 40.8 cm

Step-by-step explanation:

Given : Following shapes

To find : The perimeter of the shapes?

Solution :

For ii) part

We have to divide the shape into two regions - Rectangular Region and Semi-circular region

Rectangular Region:

Length of the Rectangle = l = 17 m

Width of the Rectangle = w = 5 m

Perimeter of the Rectangle = 2× ( l + w )

Perimeter of the Rectangle = 2× ( 17 + 5 )

Perimeter of the Rectangle = 2× 22

⇒ Perimeter of the Rectangle = 44 m

Semi-Circular Region:

∵ Length of the Rectangle corresponds to the diameter of the circle,so

Diameter of the semi-circle = d = 17 m

Radius of the semi-circle = r = 17/2 = 8.5 m

Perimeter of the Circle = 2πr

Perimeter of the Semi-Circle = 1/2(2πr)

Perimeter of the Semi-Circle = πr

Perimeter of the Semi-Circle = (3.14)(8.5)

⇒ Perimeter of the Semi-Circle = 26.69 m

Perimeter of the Shape = 44 m + 26.69 m - One Common side

Perimeter of the Shape =  70.69 m - 17 m

Perimeter of the Shape = 53.69 m

For iii) part

The radius would be 8 cm that can be seen from the fig.

so, r=8 cm

There are 2 semi circles whose radii are same.

The formula for perimeter of semi circle is pi r

The formula for perimeter of rectangle is 2(l+b)

Here l=16 cm and b=3 cm

Perimeter(P)=πr+2(l+b) +πr

P= 3.14 × 8 + 2(16+3) + 3.14 × 8

Perimeter of the shape = 88.24 cm

For iv) part

Perimeter of a semicircle= πr

Where r is the radius of a circle .

Area of a rectangle = 2 (L + B)

Where L is the length and B is the breadth .

As shown in the figure .

Radius of a big semicircle = 8/2=4 cm

Radius of a small semicircle = 4/2=2 cm

As the rectangle given in the figure is of length of 8 cm and breadth is 3 cm.

Thus,

Total Perimeter = Perimeter of a big semicircle + Perimeter of a small semicircle + Perimeter of a rectangle .

P= 3.14 × 4 + 3.14 × 2 + 2 × (3 + 8)

P= 12.56 + 6.28 + 2 × 11

P =  12.56 + 6.28 + 22

P= 40.8 cm (Approx)

Perimeter of the shape is 40.8 cm .

Answer 2

Answer:

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Step-by-step explanation:

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