how to find the perimeter of a semicircle

In Perimeter of circle lesson, we are going to discuss,

Perimeter of semicircle
Perimeter of quarter circle
Perimeter of sector

What is the Perimeter of Circle

Before moving into perimeter let's recall some knowledge about key features of circle.

Center of Circle
Diameter of Circle
Radius of Circle

Center of Circle

perimeter of circle - center

The center is the exact midpoint of the circle.

In other words, we can also define the Center as the point at which the axis of symmetry of a circle intersects is the center.

perimeter of circle - center 2

Diameter of Circle

Diameter of circle

Diameter is a straight segment joining two points on a circle, which passes through the center of the circle.

In this circle, A B is the diameter.

Radius of Circle

Radius of circle

The straight line segment joining the center to any point on the circle is called a Radius of a circle.

If the center is 'O' and the point on the circle is 'B' then, OB is the radius of the circle.

OB and OD are 'Radii' (plural form of the radius.) of the circle.

There is a relationship between diameter and radius

Diameter of circle

Diameter – AB

Radii – AO and BO

AB = AO + BO

AB = AO + AO ; because BO = AO

AB = 2 AO

Diameter = 2 x radius

The diameter of a circle is twice it's radius.

The simple meaning of perimeter is length around a closed plane figure

When it comes to circles we also called it the circumference of circle

Circumference

Circumference Formula

For full circle

Full circle formula

If 'O' is the center and 'r' is the radius of this circle.

The circumference 'c' will be,

Here π is a constant value.

pii equal

Find the circumference of a circle of radius 14cm.

Circumference c = 2π r

$example 01 math$

Therefore the circumference is 88cm.

When the diameter is given instead of the radius we have another circumference equation.

Let 'd' be the diameter and 'r' is the radius.

d = 2πr (two times radius equal to diameter)

If the circumference of the circle denoted by 'c'

c = 2πr

We can also write circumference of a circle formula as,

c = 2πr

c = π x d (d = 2πr)

c = πd

Find the circumference of a circle of diameter 21cm.

This example is about the diameter to circumference.

$Circumference example math$

Therefore the circumference is 66cm.

Exercise 01

Find the circumference of the circle with the measurements given below.

Radius 7cm
Diameter 28m (hint: convert into mixed number)
Diameter 17 1/ 2 cm
Radius 10.5m

*Answers are given at the end of this article.

Perimeter of Semicircle

perimeter of semi circle

When a circular lamina separated into two equal parts along a diameter each part is known as a semicircle.

arc and diameter

The arc length of the semicircle of radius

The arc length of the semicircle of radius

It is clear from the figure that, to find the perimeter of a semicircle, the diameter should be added to the arc length.

The perimeter of a semicircle of radius

Find the perimeter of semicircle when the diameter is 21cm.

Example 03

$arc length example math$

Therefore the perimeter of the semicircle

Exercise 02:

Find the perimeter of the semi-circular lamina with the measurements given below.

Radius = 14cm
Diameter = 7cm

*Answers are given at the end of this article.

Perimeter of Quarter Circle

perimeter of quater circle

The arc length of the quarter circle

$arc length of quarter circle math$

It is clear from the figure that, to find the perimeter of a quarter circle, two radii should add to the arc length.

The perimeter of quarter circle

$perimeter of quater circle math$

If the radius is 28cm, find the perimeter of the quarter circle.

find the perimeter of the quarter circle.

$perimeter of the quarter circle math example$

$perimeter of the quarter circle math example 1.1$

Therefore the perimeter of the quarter circle

Perimeter of a Circle Sector

A region bounded by two radii and an arc is called a sector of a circle.

The angle subtended at the center of the circle by the arc is called the central angle.

Here the central angle is 'θ '

360 angle

The angle at the center of the circle is 360^o . The arc length related to the 360 ^o angle is 2π r.

By looking at the above diagram we can say that,

For 360 ^o the arc length will be 2π r.

$Perimeter of a Circle Sector math$

arc length

The arc length of a sector of a circle with radius 'r' and central angle 'π' .

$Perimeter of a Circle Sector math 1$

example 5

$arc length example math 2$

Arc length is 11cm.

Therefore the perimeter of the sector

= 11cm + 2 x 9cm

= 11cm + 18cm

= 29cm

Answers

Exercise 01

exercise answer 1

exercise answer 2

exercise answer 3

exercise answer 4

Exercise 02

exercise 2 answer 1

exercise 2 answer 2

Calculator for Semi Circles - Area and Perimeter

Using this calculator, you can find the area and perimeter of semi-circles.

Radius, diameter, Perimeter and area calculation option are available. Select what you need to find and enter the number in text box. Then click 'submit'.

Always remember this calculator is only checking for your answers. You have to do the exercises your self.