Area - Definition with Examples

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What is Area?

In geometry, the area can be defined as the space occupied by a flat shape or the surface of an object.  
The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units such as square centimteres, square feet, square inches, etc.

The area of the squares below, with unit squares of sides 1 centimeter each, will be measured in square centimeters (cm²).

Unit squares in area in square centimeters

Here, the area of the shapes below will be measured in square meters (m²) and square inches (in²).

Unit squares in area in square meters and square inches

The origin of the word area is from ‘area’ in Latin, meaning a vacant piece of level ground. The origin further led to an irregular derivation of area as ‘a particular amount of space contained within a set of boundaries’.

We often find the area of the room floor to determine the size of the carpet to be bought. Covering the floor with tiles, covering the wall with paint or wallpaper or building a swimming pool are other examples, where in the area is computed. 

Common simple shapes and polygons have their own formulae for calculating area. Here’s how area of common 2-D or Two-dimensional shapes is computed:
Two-Dimensional Geometric Shapes:
Name of the shape: Picture of shape: Area Formula:
Circle circle
Area = πr²,
where r is the radius. 
Triangle Triangle
Area =  image bh,
where b is base,
And h is height.
Square Square
Area =l × l,
where l is the length of each side.
Rectangle Rectangle
Area = l × w,
where l is length
and w is width. 
Parallelogram Parallelogram
Area = b × h, 
where b is base,
and h is perpendicular height.
Trapezium Trapezium
Area=  image 1 (a +b)h ,
where a and b are lengths of the parallel sides,
and h is perpendicular height. 

In real life, not every plane figure can be clearly classified as a rectangle, square or a triangle. To find the area of a composite figure which consists of more than one shape, we need to find the sum of the area of both or all the shapes forming the composite figure.  

The area of the outside surface of a solid or three-dimensional shape is called Surface Area. For instance, a rectangular prism has 6 rectangular bases and lateral faces. So, the total surface area is the sum of the areas of all the 6 rectangles. 

  Fun Facts

  • Among all the shapes with same perimeter, a circle has the largest area.

let's sing Let's sing!

To plant vegetables in the garden backside,
Find the area of the field – the whole of inside.
Multiply its length with how much it is wide,
And, that’s the area formula, you have applied!

let's do it Let's do it!

Instead of handing out math worksheets on the area to your children, involve them in home improvement projects. Inform them about the room that you are considering to paint. Ask them to calculate the total surface area of the walls, in order to find how much paint is required. 

Discuss how all walls of the room may be different and thus, taking overall measurements and then subtracting the area of the door, windows or book shelves, will help in estimating the amount of paint needed. 
You can also ask to consider finding the total surface area of a present that they wrapping in order to find the amount of wrapping paper required. 

related math vocabulary Related math vocabulary

PerimeterPolygonSquare Unit, Unit Square 

Frequently Asked Questions

  • What is the area in geometry?

    In geometry, an area can be defined as the total space inside a shape. The area of a shape is the number of unit squares that cover the surface of the shape.

  • What is the unit of area?

    The area of a shape is the number of squares required to cover it completely. That is why the area is measured in square units such as square centimeters, square feet, square inches, etc.

  • Where do we use the area in real life?

    There are many instances in real life where we use the area, like finding the floor area to find the right size carpet or to cover it with tiles. We also find the area of the wall while painting or covering it with wallpaper.

  • How to introduce the concept of finding the area to a child?

    1. Ask the child to take any shape (say square or rectangle) and trace the image on a grid paper made of small squares. 2. Ask the child to count the number of squares covered by the shape. 3. The last step is to explain to the child that the number of squares counted is the space or the area occupied by the shape.

Practice Problems on Area

Pick the correct answer
1.   The perimeter of a square is 32 cm. Find its area.
2.   Which will be the most suitable unit to measure the area of an island?
3.   An equilateral triangle of side 12 cm is made using a piece of string. The same string is then used to form a square. What will be the area of this square?
4.   Area of a rectangle = ____
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