# Area Formulas

The measurement of the space encircled by a closed geometric shape is known as the area. A two-dimensional surface’s area is its actual size. Area Formulas are used extensively in research, agriculture, building, and other fields. A geometrical figure’s area can be calculated by laying it on a grid and counting the number of squares that completely encircle the figure. A shape’s area can be calculated by contrasting it with squares of a known size. The square metre, which is the size of a square whose sides are one metre long, is the common unit of area in the International System of Units (SI). The area of a shape equal to three of these squares would be three square metres.

## Area Formula

The area of any other shape or surface is a dimensionless real number, and the unit square is defined in mathematics to have area one. The areas of basic shapes like triangles, rectangles, and circles can be calculated using a number of well-known Area Formulas. By splitting a polygon into triangles and using these methods, the area of any polygon can be determined. Calculus is typically needed to calculate the area of shapes with curved boundaries. In fact, one of the main driving forces behind the historical development of calculus was the issue of estimating the area of plane figures. Area is significant in contemporary Mathematics. Aside from its obvious significance in Geometry and Calculus, area is also a fundamental characteristic of surfaces in Differential geometry and is connected to the definition of determinants in Linear algebra. In higher Mathematics, area is typically thought of as a specific instance of volume for two-dimensional regions.

The area is the measurement of space bounded by a closed geometric form. There is a collection of area formulas for polygons that may be stated using algebraic expressions.

For example, if you want to determine the area of a square and triangle boxes, you will use the following formula:

Area of Square = a2, where a is the side of the square.

Similarly,

Area of Triangle = (1/2 × b ×h)

## List of Area Formulas

Area Formulas for various geometrical figures:

 Figures Area Formula Variables Area of Rectangle Area = l × w l =  length w  = width Area of Square Area  = a2 a = sides of the square Area of a Triangle Area = 1/2 b×h b = base h = height Area of a Circle Area = πr2 r = radius of the circle Area of a Trapezoid Area = 1/2 (a + b)h a =base 1 b = base 2 h = vertical height Area of Ellipse Area = πab a = radius of the major axis b = radius of the minor axis

## Area Formula Solved Example

Example 1: Calculate the area of a rectangular building whose length and breadth are 80m and 100m respectively?

Solution:

To find: The area of a rectangular building.

Given:

Length of the building = 80m

Breadth of the building= 100m

Using area formula,

Area of Rectangle = (L × B)

= (80 × 100) m

= 8000 m2

Answer: The area of the rectangular building is 1800 m2.

Example 2: Calculate the area of a square box with each side of 8 units?

Solution:

To find: The area of a square box

Given:

Each Side of square = 8 units

We have, using area formula for square,

Area of a square = (Side)2

Area of a square = (8)2

= 64 square units

Answer: The area of square box is 64 square units.

Example 3: Find the area of a circular plate whose radius is 500m?

Solution:

To find: The area of a circular park.

Given:

Radius of the circular plate= 500m

Using area formula,

Area of a Circle = πr2

Area of a Circle = π (500)2

= 250000π m2

Answer: The area of the circular plate is 250000π m2.

Extramarks provides a list of Area formulae to help students memorise the relevant formulae. The list of Area Formulas is available on the Extramarks website and mobile app.

## FAQs (Frequently Asked Questions)

### 1. What is meant by the area of any shape?

The term “area” refers to the region enclosed by any closed figure.

### 2. What is the area of an equilateral triangle?

Area of equilateral triangle = √3/4 a2

where a is the length of the side of the equilateral triangle.

### 3. What is the area of an isosceles triangle?

Area of isosceles triangle = b/4[4a2 – b2]1/2

where a is the length of the equal sides and b is the length of the unequal side.

### 4. What is a trapezium's area?

Area of a trapezium = ½ h(a + b)

where h = height and a, b are length of the parallel sides.