Area Formulas in Maths (original) (raw)

Last Updated : 23 Jul, 2025

Area refers to the amount of space inside a shape or surface. The area of a shape can be determined by placing the shape over the grid and counting the number of squares that itcovers. Various shapes have various formulas to calculate the area, known as 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.

Given below is the different area formulas chart for various 2d shapes.

Area-Formulas

Area Formulas for various 2d shapes

Area is measured in square units. The SI unit to measure the area is m 2 .

Here we will learn about various area formulas for 2d shapes as well as 3d shapes along with their solved examples.

Table of Content

Area Formulas of 2D Shapes

Shapes that have only two dimensions are called **2-D shapes. They are drawn in 2-D space and are dependent on **2 parameters, generally length(l) and breadth(b). The various 2-D shapes are **Rectangle, Square, Triangle, Circle, and others.

Area of 2D shapes formulas are the formulas that are used to find the area of various 2D shapes, such as the area of a triangle, area of a square, area of a rectangle, area of a rhombus, etc. These area formulas are highly used in mathematics to solve various geometrical problems. Various area formulas for various shapes are,

Area Formula of a Rectangle

**It 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.

The formula for calculating the area of a rectangle is length **l and breadth **b is,

Area Formula of a 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.

The formula for calculating the area of a square with side **a is,

Area Formula of a Triangle

A triangle is the simplest polygon that is made by joining three straight lines. 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.

The formula for calculating the area of a triangle with base **b and height **h is,

Area Formula of a Circle

**Circleis a geometrical figure with no straight lines. It is the locus of the point that is always at a constant distance from the fixed point. The fixed point is called the center of the circle, and the fixed distance is the radius of the circle.

The formula for calculating the area of a circle with r as the radius of the circle is,

Area Formula of a Parallelogram

**A **Parallelogram **is a 2-D figure in which the opposite sides are parallel and equal. The formula for calculating the area of a parallelogram with base **b and height **h is,

Area Formula of a Rhombus

**A **Rhombus is a quadrilateral with all four sides equal and parallel, but not all angles are equal. The formula for calculating the area of a rhombus with diagonals **d 1 and **d 2,

Area Formula of a Trapezoid

Trapezoid is another name of trapezium. It is a quadrilateral in which the opposite sides are parallel. The formula for calculating the area of a trapezoid with parallel sides **a and **b and height **h is,

Area Formula of an Ellipse

**An **Ellipse is a 2-D shape and comes under conic sections. The formula for calculating the area of an ellipse with axes **a and **b,

Area Formula of a Semicircle

**A **Semicircle is a 2-D figure that is half of a circle. The formula to calculate the area of a semicircle with radius r is,

Area Formulas Table

The formulas for the areas of the various 2-D figures are added in the table below.

Area of Shape **Area Formula **Variables
**Area of a Rectangle Area = l × b l is the lengthb is the breadth
**Area of Square Area = a 2 a is the side of the square
**Area of Triangle Area = 1/2 × bh b is the baseh is the height
**Area of Circle Area = πr2 r is the radius of the circle
**Area of Trapezoid Area = 1/2 × (a+b)h a is the first baseb is the second base
**Area of Rhombus Area = 1/2 × d1 × d2 d1 is the One Diagonald2 is the Second Diagonal
**Area of Parallelogram Area = b × h b is the baseh is the height
**Area of Ellipse Area = πab a is the radius of major axisb is the radius of minor axis

Area of 3D Shapes Formula

**3-D shapes are the shapes that are **drawn in 3-D spaces. They have 3 dimensions that are their parameters. The area of these shapes is dependent on the length, breadth, and height of 3-D shapes. Various 3-D shapes are Cube, Cuboid, Cylinder, Cone, Sphere, and others.

The area of 3-D shapes is of two categories that are

The CSA is the area of all the curved surface of the 3-D shapes and TSA is the area of all the faces of the 3-D shapes.

Surface-Area-Formulas-(1)

Surface Area formula for 3D shapes

Area of the 3-D shapes are the space occupied by all the faces of the figure. It is **measured in units 2. The SI unit of area is m2. The area of cube, area of cuboid, area of cylinder, area of cone, and others **a in the area of 3D shapes. The table added below shows the formulas of various 3-D figures.

Area of Shape Surface Area Parameters
Area of Cube 6a2 a is the Length of the Edge
Area of a Cuboid 2(lb + lh + bh) l is the Length of the Edgeb is the Breadth of Edgeh is the Height of the Edge
Area of Cone πr(r + l) r = radius of circular basel = slant height
Area of Cylinder 2πr(r + h) r = radius of circular baseh = height of the cylinder
Area of Sphere 4πr2 r is the Radius of the sphere
Area of Hemisphere 3πr2 r is the Radius of the hemisphere
Area of Rectangular Prism 2(wl + hl + hw) l is the Length of the Edgew is the Width of the Edgeh is the Height of the Edge

**Related Articles:

Solved Examples of Area Formulas

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

**Solution:

Given,

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 Triangle(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

Conclusion

**Area formulas allow us to accurately calculate the amount of space enclosed by different geometric figures, such as rectangles, squares, circles, and more complex shapes like cubes and spheres. Mastery of these formulas is essential for solving mathematical problems and is widely utilized in fields such as engineering, architecture, and design. By using these area formulas, one can efficiently determine **areas for practical applications, ranging from **calculating the space of a room to designing architectural structures.