Area Formula

Space or region enclosed by a closed geometric figure in 2-D plane is called the area. Also, it is a quantity that expresses the extent of a two-dimensional figure or shape or planar lamina, in the plane. Area formulas are used to calculate the space enclosed by different geometric figures. The geometric area formulas are applicable to regular geometric figures having defined dimensions. 

What are Area Formulas?

Different Area Formulas are used to calculate the area of different geometric figures. A few of the important geometric figures are square, rectangle, circle, triangle, trapezoid, ellipse.

Area Formula For Triangle:

The area of a triangle can be calculated by finding the half of the product of the length of its base and height. The area of a triangle formula is given as,

Area of a Triangle = 1/2 × Base × Height

Area Formula For Square:

The area of a square is calculated by finding the square of the length of square's each side. The area of a square formula is given as,

Area of Square = Side × Side = Side²

Area Formula For Circle:

The area of the circle can be calculated b finding the product of pi with the square of the radius. The area of a circle formula is given as,

Area of a Circle = πr²

Area Formula For Rectangle:

The area of a rectangle is calculated by multiplying the length and breadth of a rectangle. The area of a rectangle formula is given as,

Area of Rectangle = Length × Breadth

Area Formula For Parallelogram:

The area of a parallelogram can be calculated by multiplying the base and height of a parallelogram. The area of a parallelogram formula is given as,

Area of a Parallelogram = Base × Height

Area Formula For a Rhombus:

The area of a rhombus can be calculated by finding half of the product of lengths of its diagonals. The area of a quadrilateral formula is given as,

Area of a Rhombus = 1/2 × Diagonal\(_1\) × Diagonal\(_2\)

Area Formula For a Trapezoid:

The area of a trapezoid is half of the product of sum of parallel sides and height. The area of a trapezoid formula is given as,

Area of a Trapezoid = 1/2 × Sum of Parallel Sides (a + b) × Height(h)

Area Formula For Ellipse:

The area of an ellipse is the product of pi with a major axis and minor axis. The area of an ellipse formula is given as,

Area of Ellipse  = π × Major axis(a) × Minor Axis(b)

Let us learn geometric area formulas for different shapes using the below-solved examples.

Examples Using Geometric Area Formula

Example 1: What is the area of a rectangular park whose length and breadth are 60m and 90m respectively?

Solution: 

To find: The area of a rectangular park.

Given:

Length of the park = 60m

Breadth of the park = 90m 

Using area formula,

Area of Rectangle = (L × B)

= (60 × 90) m² 

= 5400 m²

Answer: The area of the rectangular park is 5400 m².

Example 2: What is the area of a circular park whose radius is 400m?

Solution: 

To find: The area of a circular park.

Given:

Radius of the circular park = 400m

Using area formula,

Area of a Circle = πr²

Area of a Circle = π 400²

= 160000π m²

Answer: The area of the circular park is 160000π m².

Example 3: What is the area of a square with each side measuring 5 units?

Solution: 

We have, using area formula for square,

Area = 5 × 5 = 25 square units

Answer: The area of square is 25 square units.