Area of Shapes (original) (raw)

Last Updated : 23 Jul, 2025

Area is the space occupied inside by the boundary of any figure. It is the total surface covered by the perimeter of the figure. It is measured in square units. It is generally calculated by multiplying the bases of the figure with its length. For example, the area of the room is its length multiplied by its breadth.

In this article we will be learning about, some figures and their areas like the square, rectangle, circle, triangle, and others.

What are Area Formulas?

Area formulas are essential tools used in mathematics to calculate the amount of space enclosed by different two-dimensional shapes. These formulas can be used to find the area of geometric figures such as squares, rectangles, circles, triangles, trapezoids, and ellipses. By using these formulas, we can accurately calculate the area of different shapes, enabling us to solve real-world problems and make important calculations.

Area Formula for Rectangle:

Rectangle is a 2-Dimensional figure which is a quadrilateral, i.e. it has four sides its opposite sides are parallel and equal. All the angles in the rectangle are equal and their measure is 90 degrees. The diagonals of the rectangle are equal and they are perpendicular bisectors of each other.

**Rectangle Formula:

The formula for calculating the area of a rectangle is,

where
**l is the length of the rectangle
**b is the breadth of the rectangle

Area Formula for Square:

Square is a 2-Dimensional figure which is a quadrilateral, i.e. it has four sides its opposite sides are parallel and all four sides in a square are equal. All the angles in the square are equal and their measure is 90 degrees. The diagonals of the square are equal and they are perpendicular bisectors of each other.

Area of Square

**Square Formula:

The formula for calculating the area of a square is,

where **a is the side of the square.

Area Formula for Triangle:

Triangle is the simplest polygon which is made by joining three straight lines. As the name suggests it is a polygon with three angles. The sum of the lengths of all sides of the triangle is the perimeter of the triangle and the space inside the perimeter of the triangle is the area of the triangle.

Triangle Formula:

The formula for calculating the area of a triangle is,

where
**a, b and c are the sides of the square.
**h is the height of the square

Area Formula for Circle:

Circle is a geometrical figure with no straight line. It is the locus of the point that is always at a constant distance from the fixed point. The fixed point is called the centre of the circle and the fixed distance is the radius of the circle.

Circle Formula:

The formula for calculating the area of a circle is,

where
**r is the radius of the circle

List of Formulas:

The list of formulas for the areas of the various figures are,

**Figures **Formula **Variables
**Rectangle Area = l×b l is the lengthb is the breadth
**Square Area = a2 a is the side of the square
**Triangle Area = 1/2×bh b is the baseh is the height
**Circle Area = πr2 r is the radius of the circle
**Trapezoid Area = 1/2×(a+b)h a is the first baseb is the second base
**Ellipse Area = πab a is the radius of major axisb is the radius of minor axis

Examples of Area Formulas Using Different Geometric Shapes

**Example 1: Find the area of a rectangle with a length of 5 cm and a breadth of 2 cm.

**Solution:

Given,

Length of the Rectangle (l) = 5 cm
Breadth of the rectangle (b) = 2 cm

Area of Rectangle(A) = l × b

A = 5cm × 2cm
= 10cm2

**Example 2: Find the area of the square park whose side is 4 m.

**Solution:

Given,

Side of Square (a) = 4 m

Area of Square = a2
= (4)2 = 16 m2

Thus, the area of the square park is 16 m2

**Example 3: Find the area of a triangular plate whose height is 6 cm and the base is 6 cm.

**Solution:

Given,

Height of Triangle (h) = 6 cm
Base of Triangle (b) = 8 cm

Area of Triabgle(A) = 1/2(b × h)

A = 1/2(8 × 6)
= 48/2 = 24 cm2

The area of the triangular plate is 24 cm2

**Example 4: Find the area of a circular disc with a radius of 1.4 cm.

**Solution:

Given,

Radius of Circle (r) = 1.4 cm

Area of Circle(A) = πr2

A = π(1.4)2
= 22/7(1.4)(1.4) = (4.4)(1.4)
= 6.16 cm2

The area of the circular disc is 6.16 cm2