Circle Formula and Area Formula

Circle Formula

We may have come across many objects in our daily life which is round in shape. Some objects of this shape are wheels of a vehicle, bangles, dials of clocks, coins, etc. In a clock, we have observed that the second’s hand goes around the dial of the clock. It is making a round path around the fixed pivot. This pivot is known as a circle. This path traversed by the tip of the second’s hand is called a circle. In this article, we will discuss circles, some other related terms and circle formula with examples. Let’s start learning!

Circle Formula

What is a circle?

A circle is a particular shape of the objects. A circle is a type of closed shape. It is the set of all points in a plane that are at a given distance from a given point. So, it is the curve traced out by a point that moves in a plane in such a way so that its distance from the given point is constant.

It is defined as the set of points in a plane placed at the equal distance from a single pivot point, called the center of the circle. It is a fact that the circle represents a two-dimensional plane. Its three-dimensional figure is known as a sphere. In this shape, no vertex or edge exists.

Some terms related to this shape are as follows:

1. Center: It is a point as a pivot in the circle. It is used to draw the circle.
2. Circumference: It is the set of points that are at equal distance around the center of the circle.
3. Radius: It is the distance from the center to any point on the circumference.
4. Diameter: It is the distance between any two points on the circumference measured through the center. It is double in the length that the length of the radius.
5. Area: Area of the circle describes the amount of space covered by the circle. So, it will give the coverage of circle as a two-dimensional plane.

Diagram:

Source: en.wikipedia.org

 Where,

r	the radius of the circle.
d	the diameter of the circle.
C	circumference of the circle.

Circle Formula:

1. The diameter of the Circle is computed as,

D = 2 × R

Where,

D	The diameter of a Circle
R	Radius of circle

2. Circumference of the circle is computed as,

C = 2 × π × R

Where,

C	Circumference of circle
R	Radius of circle

3. Area of the circle is computed as,

A = π × R2

Where,

A	Area of circle
R	Radius of circle

Solved Examples on Circle Formula 

Q. A circular ground has a diameter of 800 m. Calculate the area of the circle.

Solution:

First we have to find radius of the circle as,

R = D2

i.e R = 8002

R = 400 m

Now,

Area of circular ground,

A = π × R2

= π × (400)2

=  227 × 400 × 400

= 502857.14 sq m

1. Find the area of the circle with length of circumference as 440 cm.

Solution:

First find the radius of the circle as,

C= 2 × π × R

i.e. R = Undefined control sequence \(

= 4402×722

= 70 cm

Now, find the area of the circle as,

A = π × R × R

= \frac{22}{7} × 70 × 70

=15400 sq cm.

Area Formula

The area is the size of a two-dimensional surface. The area of a plane surface is a measure of the amount of space on it. Calculating areas is a very important skill used by many people in their daily work. Like builders and tradespeople often need to work out the areas and dimensions of the structures. Also, architects, designers, and engineers are in need of area computation for their work. This article will define the term area, some common area formulas based on the shape, and also some examples. Let us get started!

Area Formula

What is Area?

The mathematical term ‘area’ can be defined as the amount of two-dimensional space covered by an object. This area calculation has many practical applications in building, farming, and architecture and also in science. Also, we need to calculate the area of walls in our room for deciding the amount of paint required. The area of an object is entirely dependent on its shape and size. We can compute the area of many common shapes by using certain accepted formulas.

Area Formulas

Let’s have a look at the most common formulas for finding the area.

1. To find the area of a rectangle shape, we use the formula:

A = L × B

Where,

A	Area
L	Length
B	Breadth

2. To find the area of a square shape, we use the formula:

A = S × S,

Where,

A	Area
S	Side

3. To find the area of a triangle shape, we use the formula:

A = 12× B × H

where

A	Area
B	Base Length
H	Height

4. To find the area of a circle shape, we use the formula:

A = π × R × R,

Where

A	Area
R	Radius

5. To find the area of a parallelogram shape, we use the formula:

A = B × H

Where,

A	Area
B	Base Length
H	Vertical Height

6. To find the area of a Trapezoid shape, we use the formula:

A =12×(S1+S2)×H

Where,

A	Area
S1	First parallel side length
S2	Second parallel side length
H	Vertical Height

Remember that the unit of the area will be in the “square unit” of the length unit.

Solved Examples

Let us have some examples of finding the area.

Q: Find the area of a square board whose side measures 120 cm.

Solution:

Side of the board = 120 cm

Area of the board = side  × side

= 120 cm  ×120 cm

= 14400 sq. cm

Q: A courtyard’s floor is 50 m long and 40 m wide. It has to be covered by some square tiles. The side of each tile is 2 m. Compute the number of tiles required to cover the floor.

Solution: First we have to calculate the area of the courtyard. Then we will calculate the area of one tile,

Length of the rectangular floor = 50 m

The breadth of the rectangular floor = 40 m

Area of the floor = Length × Breadth

= 50 m × 40 m

= 2000 sq. m

Now, side of one square tile = 2 m

Area of one tile = Side × Side

= 2 m  × 2 m

= 4 sq. m

Thus, number of tiles needed to cover the floor,

=  AreaofFloorAreaofoneTile

=  20004

= 500 tiles