Area

Area is the measure of the space occupied by the boundary of the shape. It is the total space occupied by the given figure and it is measured in unit square. The number of the unit square covered inside the figure is referred to as the area of the figure. The standard unit of the area is unit², i.e. m², cm², etc. 

In this article, we will learn about, what is the area, its unit, areas of various shapes, areas of complex shapes, solved examples related to the area, and others in detail.

What Is Area?

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.

Area of any figure is a two-dimensional quantity and it is measured in the unit squares, i.e. we measure the area of the figure in m², cm², ft², etc. The area of any figure is dependent on the sides and the height of the figure.

Area of Shapes

The area of various shapes is used to solve different problems in Geometry, there are various shapes whose area we can easily find and the area of various figures depends on various parameters. We calculate the area of different shapes by using two methods that include,

• Area of Simple Shapes
• Area of Complex Shapes

Now let’s learn about them in detail

Area of Simple Shapes

Simple shapes are regular shapes and some common simple shapes include squares, rectangles, triangles, circles, and trapezoids. 

• The area of a square is equal to the square of its side length. 
• The area of a rectangle is equal to its length multiplied by its width. 
• The area of a triangle is equal to one-half the product of its base and height. 
• The area of a circle is equal to π multiplied by the square of its radius. 
• The area of a trapezoid is equal to one-half the sum of its bases multiplied by its height.

The area formula for some simple shapes is,

• A square is a regular polygon with four sides and the formula for the area of the square is,

Area of Square = a² units²

where a is the length of the square

• A rectangle is a polygon with four sides in which the opposite sides are parallel and equal and the formula for the area of the rectangle is,

Area of Rectangle = l.b units²

where, 

• l is the length of the rectangle
• b is the base of the rectangle

• A triangle is a polygon with three sides it is the simplest polygon possible and the formula for the area of the triangle is,

Area of Triangle = 1/2×b×h units²

where,

• b is the base of the Triangle
• h is the Height of the Triangle

• A circle is a curved figure in which the distance of the curve is always fixed from the center of the curve. The formula to calculate the area of the circle is,

Area of Circle = πr² units²

where, r is the radius of the Circle

Area Units

The area of any figure is nothing but the space occupied by the sides of the polygon. So the area is measured in units², i.e. m², cm,² etc. If the given figure or structure is very large its area can also be measured in Kilometers² or any other unit².

How to Find Area?

To find the area of any figure we use the steps discussed below:

Step 1: Find the length of all the sides of the given figure and the height of the figure.

Step 2: Find the area using the various area formulas.

Step 4: As the area is a 2-dimensional figure then the area is measured in unit²

For example, suppose we have to find the area of a square plot of side 10 m.

Solution:

Side of Square (a) = 10 m

Area of Square(A) = a²

A = (10)² = 100 m²

Thus, the area of the square feild is 100 m²

Area of Complex Shapes

The area of a complex shape is the amount of space enclosed by the shape. Complex shapes do not have a regular shape and cannot be easily divided into smaller shapes with known areas. To find the area of a complex shape, it is often necessary to break the shape down into smaller, simpler shapes. The areas of the smaller shapes can then be added together to find the area of the complex shape.

For example, the area of the following shape can be found by breaking it down into a rectangle and a triangle:

Solution:

The complex figure is broken into a rectangle and a triangle as shown in the figure,

Thus, the area of the complex figure is,

Area of the Rectangle = l.b = 10×6 = 60 m²

Area of the Triangle = 1/2.b.h = 1/2.10×6 = 60 m²

Area Formulas

The formula to calculate the area of various figures is,

Name	Area	Parameters
Circle	πr2	r = Radius of the circle
Triangle	(½)bh	b = Base h = Height
Square	a2	a = Length of the side
Rectangle	l.b	l = Length b = Breadth
Rhombus	(½)d1d2	d1 and d2 are the lengths of two diagonals
Parallelogram	bh	b = Base h = Height (distance between two parallel bases)

Applications of Area

Area has a wide variety of applications in mathematics, science, engineering, and other fields. Some common applications of the area include:

• Geometry: Area is used in geometry to find the size of regions.
• Physics: Area is used in physics to find the amount of surface area exposed to a given force.
• Engineering: Area is used in engineering to find the amount of material needed to build a structure.
• Architecture: Area is used in architecture to find the size of rooms and other spaces.
• Geography: Area is used in geography to find the size of countries, states, and other land masses.
• Planning: Area is used in planning to find the size of parks, playgrounds, and other public spaces.

Examples of Area Formulas

Example 1: Find the area of a rectangle with a length of 18 cm and a breadth of 3 cm.

Solution:

Given,

• Length of the Rectangle (l) = 18 cm
• Breadth of the rectangle (b) = 3 cm

Area of Rectangle(A) = l × b

A = 18 × 3
   = 48 cm²

Example 2: Find the area of the square park whose side is 12 m.

Solution:

Given,

• Side of Square (a) = 12 m

Area of Square = a² 
= (12)² = 144 m²

Thus, the area of the square park is 144 m²

Example 3: Find the area of a triangular plate whose height is 16 cm and the base is 8 cm.

Solution:

Given,

• Height of Triangle (h) = 16 cm
• Base of Triangle (b) = 8 cm

Area of Triangle(A) = 1/2(b × h)

A = 1/2(16 × 8)
   = 128/2 = 64 cm²

The area of the triangular plate is 64 cm²

Example 4: Find the area of a circular disc with a radius of 7 cm.

Solution:

Given,

• Radius of Circle (r) = 7 cm

Area of Circle(A) =  πr²

A = π(7)²
   = 22/7(7)(7) = 22×7
   = 144 cm²

The area of the circular disc is 144 cm²

FAQs on Area

Q1: What is Area?

Answer:

Area is a measurement of the amount of space occupied by a two-dimensional shape or surface. It is typically expressed in square units, such as square centimeters (cm²) or square meters (m²).

Q2: How is Area of a Rectangle Calculated?

Answer:

The area of a rectangle is calculated by multiplying its length by its width. The formula for the area of a rectangle is A = length × width.

Q3: How is Area of a Triangle Calculated?

Answer:

The area of a triangle is calculated by multiplying its base by its height and then dividing the result by 2. The formula for the area of a triangle is A = (base × height) / 2.

Q4: How is Area of a Circle Calculated?

Answer:

The area of a circle is calculated by multiplying the square of its radius by the mathematical constant pi (π). The formula for the area of a circle is A = πr², where “r” represents the radius of the circle.

Q5: How is Area of a Square Calculated?

Answer:

The area of a square is calculated by multiplying the length of one of its sides by itself. The formula for the area of a square is A = side².

Q6: How is Area of a Parallelogram Calculated?

Answer:

The area of a parallelogram is calculated by multiplying its base by its height. The formula for the area of a parallelogram is A = base × height.

Q7: How is Area of Irregular Shapes Calculated?

Answer:

The area of irregular shapes can be calculated by dividing the shape into smaller, regular shapes (such as triangles, rectangles, or circles) and finding the area of each component. The areas of the components are then summed to obtain the total area of the irregular shape.