Perimeter of a sector of a circle calculator

In this example you are not given the angle of the sector, you need to calculate it first.

Here you can use the triangle created by the two radii and the chord to find the angle (see below):

We will need to use the cosine rule to find the angle.

a^2=b^2+c^2-2bcCos(A)

A is the angle you are trying to find. You can therefore use the rearranged cosine rule to find the angle.

\begin{aligned} \operatorname{Cos} A&=\frac{b^{2}+c^{2}-a^{2}}{2 b c} \\ \operatorname{Cos} A&=\frac{19^{2}+19^{2}-20^{2}}{2 \times 19 \times 19} \\ \operatorname{Cos} A&=\frac{161}{361} \\ A&=\operatorname{Cos}^{-1}\left(\frac{161}{361}\right) \\ A&=63.51^{\circ} \end{aligned}

The size of the angle creating the sector (made by the two radii) is 63.5^o .

In next fields, kindly type the dimensions of your shape in the text box under title [ Unknowns: ]. After you type your value, click "CALCULATE" button; the answer will be automatically calculated and displayed in the text box under title [ Answer: ]. Also, you will be able to animate your shape through buttons under the below figure.

Unknowns:RESET CALCULATEAnswer:

Perimeter:

Decimals:

Rotate: (around) X Y Z XYZ Stop reset

Figure(#): sector of circle with parameters.

How to Calculate Perimeter Of Sector Of Circle

Example: What is the perimeter of sector of circle with radius = 17 units and angle = 31 units?

As;

perimeter of sector of circle = π*radius*angle/180+2*radius

By substituting the above given data in the previous function;

(i.e.) = π*17*31/180+2*17

Answer is: units.

Practice Question: Calculate perimeter of sector of circle for the following problems:

N.B.: After working out the answer of each of the next questions, click adjacent button of see the correct answer.

A circle has always been an important shape among all geometrical figures. There are various concepts and formulas related to a circle. The sectors and segments are perhaps the most useful of them. In this article, we shall focus on the concept of a sector of a circle along with area and perimeter of a sector.

A sector is said to be a part of a circle made of the arc of the circle along with its two radii. It is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc. The shape of a sector of a circle can be compared with a slice of pizza or a pie.

Table of Contents:

• Definition
• Area of Sector
• Arc Length Formula
• Video Lessons
• Examples
• Perimeter of Sector
• Practice Questions
• FAQs

Before we start learning more about the sector, first let us learn some basics of the circle.

What is a Circle?

A circle is a locus of points equidistant from a given point located at the centre of the circle. The common distance from the centre of the circle to its point is called the radius. Thus, the circle is defined by its centre (o) and radius (r). A circle is also defined by two of its properties, such as area and perimeter. The formulas for both the measures of the circle are given by;

• • Area of a circle = πr2
  • The perimeter of a circle = 2πr

What is Sector of a circle?

The sector is basically a portion of a circle which could be defined based on these three points mentioned below:

• A circular sector is the portion of a disk enclosed by two radii and an arc.
• A sector divides the circle into two regions, namely Major and Minor Sector.
• The smaller area is known as the Minor Sector, whereas the region having a greater area is known as Major Sector.

Area of a sector

In a circle with radius r and centre at O, let ∠POQ = θ (in degrees) be the angle of the sector. Then, the area of a sector of circle formula is calculated using the unitary method.

For the given angle the area of a sector is represented by:

The angle of the sector is 360°, area of the sector, i.e. the Whole circle = πr2

When the Angle is 1°, area of sector = πr2/360°

So, when the angle is θ, area of sector, OPAQ,  is defined as;

A = (θ/360°) ×  πr2

Let the angle be 45 °. Therefore the circle will be divided into 8 parts, as per the given in the below figure;

Now the area of the sector for the above figure can be calculated as (1/8) (3.14×r×r).

Thus the Area of a sector is calculated as:

A = (θ/360)  × 22/7 × r2

Length of the Arc of Sector Formula

Similarly, the length of the arc (PQ) of the sector with angle θ, is given by;

l = (θ/360)  × 2πr   (or) l = (θπr) /180 

Area of Sector with respect to Length of the Arc

If the length of the arc of the sector is given instead of the angle of the sector, there is a different way to calculate the area of the sector. Let the length of the arc be l. For the radius of a circle equal to r units, an arc of length r units will subtend 1 radian at the centre. Hence, it can be concluded that an arc of length l will subtend l/r, the angle at the centre. So, if l is the length of the arc, r is the radius of the circle and θ is the angle subtended at the centre, then;

θ = l/r, where θ is in radians.

When the angle of the sector is 2π, then the area of the sector (whole sector) is πr2

When the angle is 1, the area of the sector = πr2/2π = r2/2

So, when the angle is θ, area of the sector = θ ×  r2/2

A = (l/r) × (r2/2)

A = (lr)/2

Video Lessons on Circles

Introduction to Circles

Parts of a Circle

Area of a Circle

All about Circles

Some examples for better understanding are discussed here.

Examples

Example 1: If the angle of the sector with radius 4 units is 45°, then find the length of the sector.

Solution: Area = (θ/360°) ×  πr2

= (45°/360°) × (22/7) × 4 × 4

= 44/7 square units

The length of the same sector = (θ/360°)× 2πr

l = (45°/360°) × 2 × (22/7) × 4

l = 22/7

Example 2: Find the area of the sector when the radius of the circle is 16 units, and the length of the arc is 5 units.

Solution: If the length of the arc of a circle with radius 16 units is 5 units, the area of the sector corresponding to that arc is;

A = (lr)/2 = (5 × 16)/2 = 40 square units.

• Area Of Sector Of A Circle
• Area of a Sector of Circle Formula
• Area of a Segment of a Circle Formula
• Segment and Areas of Segment of a Circle
• Parts of a Circle

Perimeter of a Sector

The perimeter of the sector of a circle is the length of two radii along with the arc that makes the sector. In the following diagram, a sector is shown in yellow colour.

The perimeter should  be calculated by doubling the radius and then adding it to the length of the arc.

Perimeter of a Sector Formula

The formula for the perimeter of the sector of a circle is [2r + 𝜃/360o (2𝜋r)] where r is the radius of the circle and 𝜃 is the angle of the sector.

What is the formula to find the perimeter of a sector of a circle?

What is perimeter of a sector and segment?

What is the perimeter of a sector of angle 45?

How do you find the area of a sector of a circle calculator?