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Area Formulas

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Area Formulas for various objects are the formulas that are used to find the area of various object. Area is the space occupied by the boundary of any figure. Area formulas of various geometric shapes are dependent on various parameters, such as dimensions, height, and radius of various geometric shapes. Geometric shapes are of two types that are:

  • Two-Dimensional Shapes (2-D Shapes)
  • Three-Dimensional Shapes (3-D Shapes)

In this article we will be learning about, area formulas for various 2-D and 3-D shapes such as area of rectangle, area of square, area of circle, area of of cube, etc. and others in detail.

What is Area?

The space occupied by the boundary of a figure is called area of the figure. It is measured in unit square. The SI unit to measure the area is m2. Area is used in various mathematical concepts and is also used in real life scenarios such as to find the area of room, area table, etc. and other.

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-Formulas

Area Formulas

What are 2D Shapes?

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

Area of 2D Shapes Formula

Area of 2D shapes formulas are the formula that are used to fond the area of the various 2D shapes, such as area of triangle, area of square, area of rectangle, area of 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

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.

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

  • Area of Rectangle (A) = l×b square units

Area Formula of a 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.

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

  • Area of Square (A) = a2 sq. units

Area Formula of a 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.

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

  • Area of Triangle (A) = 1/2 × bh sq. units

Area Formula of a 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 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 of Circle (A) = Ï€r2 sq. units

Area Formula of a Parallelogram

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

  • Area of Parallelogram (A) = bh sq. units

Area Formula of a Rhombus

Rhombus is a quadrilateral with all four sides equal and parallel but not all angles are equal. The formula for calculating the area of rhombus with diagonal d1 and d2 are,

  • Area of Rhombus (A) = 1/2 × d1 × d2 sq. units

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 trapezoid with parallel sides a and b and height h is,

  • Area of Trapezoid (A) = 1/2(a +b)h sq. units

Area Formula of a Ellipse

Ellipse is a 2-D shape and comes under conic sections. The formula for calculating the area of a ellipse with axis as a and b are,

  • Area of Ellipse (A) = Ï€ab sq. units

Area Formula of a Semicircle

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

  • Area of Semicircle (A) = 1/4(Ï€r2) sq. units

Area Formulas Table

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

Figures

Formula

Variables

Rectangle

Area = l×b

  • l is the length
  • b is the breadth

Square

Area = a2

a is the side of the square

Triangle

Area = 1/2×bh

  • b is the base
  • h is the height

Circle

Area = πr2

r is the radius of the circle

Trapezoid

Area = 1/2×(a+b)h

  • a is the first base
  • b is the second base

Rhombus

Area = 1/2×d1×d2

  • d1 is the One Diagonal
  • d2 is the Second Diagonal

Parallelogram

Area = b × h

  • b is the base
  • h is the height

Ellipse

Area = πab

  • a is the radius of major axis
  • b is the radius of minor axis

What are 3D shapes?

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 are dependent on length, breadth and height of 3-D shapes. Various 3-D shapes are, Cube, Cuboid, Cylinder, Cone, Sphere, and others. Area of 3-D shapes are of two categories that are Curved Surface Area (Lateral Surface Area){CSA}, and Total Surface Area(TSA). 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.

Area of 3D Shapes Formula

Area of the 3-D shapes are the space occupied by all the faces of the figure. It is measured in unit2. The SI unit of area is m2. The area of cube, area of cuboid, area of cylinder, area of cone, and others comes 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 Edge

Area of Cuboid

2(lb + lh + bh)

  • l is the Length of Edge
  • b is the Breadth of Edge
  • h is the Height of Edge

Area of Cone

Ï€r(r + l)

  • r = radius of circular base
  • l = slant height

Area of Cylinder

2Ï€r(r + h)

  • r = radius of circular base
  • h = height of the cylinder

Area of Sphere

4Ï€r2

r is the Radius of sphere

Area of Hemisphere

3Ï€r2

r is the Radius of hemisphere

Area of Rectangular Prism

2(wl + hl + hw)

  • l is the Length of Edge
  • w is the Width of Edge
  • h is the Height of Edge

Also, Check

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,

  • 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 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

Area Formulas FAQs

What are Area Formulas?

The area formulas are the formulas which are used to find the area of any figure. It is used to find the amount of space occupied by the figure. Generally, the area is represented with the letter ‘A’. and is measured in unit2, i.e. cm2, m2, etc.

What is Area Formula For Square?

The area formula for a square is the formula to calculate the space occupied by the square. The formula to calculate the area of the square is,

Area of Square = (side)2

What is Area Formula For Rectangle?

The area formula for a rectangle is the formula to calculate the space occupied by the rectangle. The formula to calculate the area of the rectangle is,

Area of Rectangle = Length × Breadth

What is Area Formula For Triangle?

The area formula for a triangle is the formula to calculate the space occupied by the triangle. The formula to calculate the area of the triangle is,

Area of Triangle = 1/2(base × height)

What is Area Formula For Circle?

The area formula for a circle is the formula to calculate the space occupied by the circle. The formula to calculate the area of the circle is,

Area of Circle = π(radius)2

What is Area Formula For Quadrilateral?

Formula to calculate the area of quadrilateral,

Area of Quadrilateral = 1/2 × Diagonal1 × Diagonal2

What is Area Formula of Triangular Prism?

Formula for area of Triangular Prism is,

Area of Triangular Prism = (Perimeter of Base × Length of Prism) + 2 × Base Area

What is Area Formula of Polygon?

The formula to calculate the area of polygon is,

Area of Polygon = 1/2 × (Perimeter × Apothem)

What is Area Formula of Right Triangle?

Formula for area of Right Angle Triangle is,

Area of Right Triangle = 1/2 × Perpendicular × Base

What is Area Formula of Pentagon?

Formula for area of Pentagon is,

Area of Pentagon = 1/2 × Perimeter × Apothem



Last Updated : 29 Feb, 2024
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