Area and Perimeter

Area and perimeter are the two important properties of 2D shapes. When we talk of the concept of Perimeter, it means the total distance of the boundary of any shape whereas the area describes the region within it. It is commonly used in daily life that it has become an important part of our activities. In this article we will learn about area and perimeter of all shapes such as rectangle, square, triangle, rhombus, difference between area and perimeter, etc.

Area and Perimeter Formulas for all Shapes

Before looking into the area and perimeter formulas for all shapes, let us look what is area and perimeter.

What is Area?

Area is the region within the shape of an object or in other terms, the space covered by the figure or any two-dimensional geometric shape, in an xy plane. This physical quantity depends on the dimensions and properties of the shape under consideration.

What is Perimeter?

The term Perimeter is defined as the total distance or length of boundary around a shape in a 2d or xy plane. It is calculated by adding the lengths of the sides of the shape. For example if we take a round of a circular park and at the end calculate the total distance covered, we get the perimeter.

Now let us look into the area and perimeter of 2D shapes.

Area and Perimeter of 2D shapes

We should note that if two objects have a similar shape then it is never compulsory that their area when calculated gives out same results. The condition to be met is that their dimension must also be equal.

For example, there are two rectangle boxes, with length as $P1$ and $P2$ and breadth as $Q1$ and $Q2$. So the areas of both the rectangular boxes, say $A1$ and $A2$ will be equal only if $P1=P2$ and $Q1=Q2$.

Area and Perimeter of Rectangle

A rectangle is a four sided shape in which opposite sides are equal and all angles measure 90 degrees.

Formula of area and perimeter of rectangle

Perimeter of a Rectangle $=2(p+q)$
Area of Rectangle $=p \times q$

Where $p,q$ are the length and breadth respectively.

Area and Perimeter of Square

A square is a shape with all four sides equal with all angles measuring 90 degrees.

Area and Perimeter of Square Formula

Area and perimeter of square is given as:

- Perimeter of a Square $=4 x$
- Area of a Square $=x^2$

Where $x$ is the side of square.

Area and Perimeter of Triangle

A triangle is a three-sided shape where the sum of all angles of the triangle is $180^{\circ}$.

Triangle area and perimeter

The area and perimeter of triangle formula is

- Perimeter of a triangle $=p+q+r$, where $p, q$ and $r$ are the three different sides of the triangle.
- Area of a triangle $=\frac{1}{2} \times b \times h$; where $b$ is the base and $h$ is the height of the triangle.

Area and Perimeter of Circle

A circle is a round geometric shape with no vertex.

Area and perimeter of circle is given as:

- Circumference(Perimeter) of Circle $=2 \pi r$
- Area of Circle $=\pi r^2$

where $ r$ is radius of circle

Area and Perimeter of Rhombus

A rhombus is a four sided shape with all equal sides.

Difference Between Area and Perimeter

Following table lists the difference between area and perimeter.

Solved Examples on Area and Perimeter

Example 1: Given the radius of a circle is 20 cm . Find area and perimeter of circle.
Solution: Given, radius $=20 \mid \mathrm{cm}$
Hence, Area $=\pi \times r^2$

$
A= \frac{22}{7} \times 20 \times 20
$

Area of circle $=1257.14$ sq.cm.
Circumference, $C=2 \pi r$
Perimeter of circle $=2 \times \frac{22}{7} \times 20=125.7 \mathrm{~cm}$
So, Area and Perimeter of circle $=1257.14$ sq. $\mathrm{cm}, 125.7 \mathrm{~cm}$ respectively.

Example 2: The length of the side of a square is 5 cm . Calculate area and perimeter of square.

Solution: Given, length of the side, $a=5 \mathrm{~cm}$
Area of square $=a^2=5^2=25$ sq.cm
Perimeter of square $=4 a=4 \times 5=20$ sq.cm.
So, Area and Perimeter of square $=25 \mathrm{sq} . \mathrm{cm}, 20 \mathrm{~cm}$ respectively.

Example 3: The length of rectangular field is 12 m and width is 6 m . Calculate the area and perimeter of rectangle.

Solution: Given, Length = 12m
Width $=6 \mathrm{~m}$
Therefore, Area of rectangle $=$ length $\times$ width $=12 \times 6=72$ sq.m.
Perimeter of rectangle $=2(1+b)=2 \times 18=36 \mathrm{~m}$.
So, Area and Perimeter of rectangle $=72 \mathrm{sq} . \mathrm{cm}, 36 \mathrm{~cm}$ respectively.

Example 4: What is the area of triangle with base 6 cm and height 10 cm ?
Solution: Area of triangle $= \frac{1}{2} \times b \times h= \frac{1}{2} \times 6 \times 10=30 \mathrm{sq} \mathrm{cm}$.

Example 5: What is the perimeter of triangle of sides $3 \mathrm{~cm}, 4 \mathrm{~cm}, 5 \mathrm{~cm}$ ?
Solution: Perimeter of triangle $=$ Sum of all sides $=3 \mathrm{~cm}+4 \mathrm{~cm}+5 \mathrm{~cm}=12 \mathrm{~cm}$.

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