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Last updated date: 09th Apr 2024
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History of Area

The first recorded use of areas was in ancient Babylon, where they used it to measure the amount of land that was owned by different populations for taxation purposes. Later in 287 BC, the great mathematician Archimedes from Greece discovered the area and the perimeter of the circle and the relationship between spheres. Archimedes, no doubt, wasn't the first to realize the fact. However, he was, as far as we know, the first to prove it formally. He also gave the earliest proofs for the volume of the sphere and surface area.

Definition of Area

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

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

To determine the size of the carpet to be bought, we often find the area of the room floor.

To cover the floor with tiles, to cover the wall with paint or wallpaper or to build a swimming pool are other examples, where the area is computed.

In reality, not every plane surface can be clearly classified as a rectangle, square or a triangle. For finding the area of a composite figure that contains more than one shape, we will find the sum of the area of all the shapes forming the composite figure.

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

Area Formulas

In general, we can say that the area of shapes can be defined as the quantity of paint required to cover the surface with a single coat. These are the following ways to calculate the area based on the number of sides that exist in the shape, as illustrated below in fig.

   (Images will be uploaded soon)

What are 3D Shapes?

The three-dimensional shapes, also known as solid shapes, are those which have three dimensions such as length, breadth and thickness. The two different measures which are used to define the three-dimensional shapes are surface area and volume. In general, the 3D shapes are obtained from the rotation of two-dimensional shapes. Thus, the surface area of any two-dimensional shapes should be a 2D shape. If we want to calculate the surface area of any solid shape, we can easily calculate it from the area of 2D shapes.


Area of 3D Shapes Formula

According to the International System of Units (SI), the standard unit of area is the square meter (written as m2) and it is also the area of a square whose sides are one meter long. For example, a definite shape with an area of three square meters would have the same area as three such squares. The surface area of any solid object is a measure of the total area which the surface of the object occupies.


For 3D/ solid shapes like cuboid, cube, cylinder, sphere and cone, the area is updated to the concept of the surface area of the shapes. The formulas for 3D shapes are given in the table below:


Area Formula for Different Shapes





π × r2

r = radius of the circle


½ × b × h

b = base

h = height



a = length of side


l × w

l = length

w = width


b × h

b = base

h = vertical height


½(a + b) × h

a & b are length of parallel sides

h = height



a = ½ minor axis

b = ½ major axis

Formulas for 3D Shapes


Surface Area




a = length of the edge

Rectangular prism

2(wl + hl + hw)

l = length

w = width

h = height


2πr(r + h)

r = radius of the circular base

h = height of the cylinder


πr(r + l)

r = radius of the circular base

l = slant height



r = radius of the sphere



r = radius of the hemisphere

Know More about Area 

The area is defined as a two-dimensional space that is taken up by an object. The concept of the area has a lot of real-life applications. For example; the area is used in farming, building, plotting lands, science and so much more like painting the walls of your room or buying new furniture for the house.  

The area can be determined with basic calculations and understanding. The number of square units inside a figure is used to find out the area for a square or rectangle. Sometimes, in the cases of polygons, one can find out the area by multiplying the length by the width.

  • To find out the area of a Square,

A=s2 where s is the length of the sides of the square. 

  • To find out the area of a Rectangle

 A=LW, where L and W are the lengths of the rectangle's sides (length and width).

  • To find out the area of a triangle

A=12bh, where b and h are the base and height.

  • To find out the area of a Parallelogram

 A=bh, where b is the length of the base and h is the height.

  • To find out the area of a Circle

A=πr2, where r is the radius

FAQs on Area

1. How to find out the area of a circle? 

To find out the area of a circle, one must understand that the circle is the total area that is bounded by the circumference of the distance around the circle. Imagine if you drew a circle, and filled the insides of a circle with colors or other objects, that is the area of a circle. The formula to find out the area of a circle is A = π x r2. Here, A is the area, R represents the radius (radius is half the distance from one side of the circle to the other) and π is  3.14 (which is a Greek letter pronounced as “pi”). The number 3.14 is the ratio of a circle’s circumference to its diameter. 

2. What is the difference between Area and Volume?



The area is the quantity of space occupied by a two-dimensional flat object in a plane.

Volume is defined as the space occupied by the 3D object.

It is always measured in square units

It is always measured in cubic units