 # Area and Perimeter

Introduction of Area and Perimeter

In our everyday life, we come across a lot of objects of varying shapes and sizes, square, triangle, rectangle, sphere, circle, rhombus, and many others. Area and Perimeter give us valuable knowledge which helps us deal with these different forms of objects.

What are Area and Perimeter?

So, what is the meaning of Perimeter and Area?

Let us see how we can define Perimeter and Area in the mathematical sense before we head to solving problems. Before getting to the trickier part of the topic, we must strengthen our conceptual understanding of Area and Perimeter -

Area - Area helps in determining the boundaries of a two-dimensional object or a plain. The term, “area” can be defined as the enclosed space within the frames of an object. This space is known as the Area of that particular shape.

Perimeter- The sum total of the distance covered along the outer part of the shape gives us the Perimeter. Again, dimension plays a major role in this too as depending on the dimensions of the shapes, the Perimeter of different shapes can be equal to each other.

How Can We Calculate Area and Perimeter?

Now that we are clear on the area and perimeter meaning in math, let us see how we can calculate the Perimeter and Area of some of the most common shapes we encounter on a daily basis.

Area and Perimeter of a Square -

A square's all four sides are equal in length and are at an identical angle if 90 degrees. Therefore, to measure the Area covered by the square and it's Perimeter, these following are the formulae to be used -

Area - a2

Perimeter - 4a

Let's take a as the length of the 4 sides.

Area and Perimeter of A Rectangle -

A rectangle is an elongated figure with its opposite sides matching in length and all the angles at an identical 90 degrees.

Rectangle's Area - a×b

Rectangle's Perimeter - 2(a+b)

Let a and b be the length and breadth respectively.

Area and Perimeter of the Triangle -

A triangle is made up of 3 sides. The Perimeter of a triangle is calculated by adding up the lengths of all 3 sides of the triangle.

Triangle's Area- ½ b×h, let b be the base and h be the height.

Triangle's Perimeter - a +b + c where all three represent the 3 sides of a triangle.

Area and Circumference of a Circle -

The circle 's Perimeter is known as the circumference.

Circumference = 2πr

Area of Circle = πr2

Area And Perimeter Chart

The following chart contains all the formulas used to calculate the Area and Perimeter of different shapes in tabular data to make it easier for you to go through.

 Shape Area Perimeter Terms Square a2 4a a =length of all four sides Rectangle a × b 2(a+b) a = length b= width Triangle ½ b×h a + b+ c b= baseh= heighta, b, c are the 3 sides of a triangle respectively Circle πr2 2πr r = represents the  circle's radius

Here are some solved perimeter and area class 5 questions with answers for you to understand better -

Q. If the given radius of a circle is 21cm. Calculate its circumference and Area.

Solution:

Therefore, Area = π × r2

A = 22/7 × 11 × 11

A = 380.28 sq.cm.

Circumference, C = 2πr

C = 2 x 22/7 x 11 = 69.14 cm

Example 2:

Q. If the given square's side's length is 4 cm. Then measure its Area and also calculate the Perimeter.

Solution:

We know, length of the side, a = 4 cm

Area = a2 = 42 = 16 sq.cm

Total length of its boundary, Perimeter = 4a = 4 x 4 = 16 sq.cm.

Example 3:

Q. A given rectangular field measures 20m in length and 30m in breadth. Calculate the Area and Perimeter.

Solution:

Given, Length = 20m

Width = 30m

Since, Area = length x breadth = 20 x 30 = 600 sq.m.

Perimeter = 2 (length + breadth) = 2 x (20 +30) = 2 x 50 = 100 m.

Did You Know -

• Two different rectangles having equal perimeter dimensions can still cover different areas.

• Squares and rectangles always cover more Area, and the Perimeter always tends to be lesser than the Area covered but in triangles, the Perimeter is more than the Area covered.

1. How is Area Different from Perimeter?

Area Vs Perimeter - The two-dimensional region enclosed in a framed figure is known as the Area.

Whereas, the distance along the outer part of the shape is known as the Perimeter.

Just because two shapes may be identical in nature and shape doesn't mean they will have equal Perimeter and Area. That is only possible when the dimensions of these two objects are equal. In some cases, you may also see that the perimeters differ, but the Area covered is the same and, in some cases, vice versa. Suppose you want to fence a region; it is important that you know the dimensions as many people get confused and believe that the Perimeter of an area remains the same despite the Area. That is not true as the shape of that Area might change the Area of Perimeter covered of the region.

2. How are Area and Perimeter Applicable in our Daily Lives?

Let us say you want the walls of your room painted. To determine the quantity of paint, you would be needing and the cost of it, you need to know the Area of your room.

Let's see another situation where you want your garden's Perimeter to be fenced, but you are unaware of the dimensions. How will you know how much material you will be required to buy for the fencing? Or say the tiles in your room have cracked in several places and you want to replace them, you would need to have knowledge about the Area covering the floor and to know the exact amount of tiles you will be needed to spend on for the entire floor.