Area of a Rectangle: An In-depth Overview

Have you ever found yourself measuring your garden, trying to figure out the best way to optimise the space? Or maybe you’re planning a home renovation and need precise area calculations. Knowing how to calculate the Area of a Rectangle is key for doing these tasks. While it might seem simple, this concept has countless practical applications in everyday life.  

In this blog, we’ll break down the Area of a Rectangle in a way that’s easy to understand. We’ll cover the formula, provide practical examples, and share tips for accurate calculations. By the end, you’ll be confident in measuring rectangular spaces, whether it’s for landscaping or arranging furniture. Get ready to tackle your rectangle-related projects with ease! 

Table of Contents 

1) What is the Area of Rectangle? 

2) Area of Rectangle Formula 

3) How to Calculate the Area of Rectangle? 

4) Area of a Rectangle using Diagonal 

5) Area of a Rectangle using Perimeter 

6) Why Area of the Rectangle is Length x Breadth? 

7) Area of Rectangle: Solved Examples 

8) What is the Perimeter of a Rectangle?

9) Conclusion 

What is the Area of Rectangle? 

The Area of a Rectangle represents the space enclosed within its four sides. In simpler terms, it’s the amount of surface area the rectangle covers. It is fundamental in geometry and plays a critical role in various practical uses, such as measuring land, room dimensions, or any rectangular object. 

A rectangle is defined by two pairs of opposite sides that are equal in length, and its interior angles are all right angles (90 degrees). The length and breadth (or width) are the two crucial dimensions that determine its area. When calculating the area, you’re essentially determining how many unit squares fit inside the rectangle.
 

Area of Rectangle Formula 

You can calculate the Area of a Rectangle easily using the formula given below:

 Formula:  

1) Length: The longer side of the rectangle. 

2) Breadth (or width): The shorter side of the rectangle. 

This formula is based on the idea that if you divide the rectangle into unit squares, the total number of squares that can fit into the rectangle equals the product of its length and breadth. 

How to Calculate the Area of Rectangle? 

To calculate the Area of a Rectangle, follow these simple steps: 

1) Measure the Length: Measure the longer side of the rectangle. For instance, if the longer side is 10 metres, then this is your length. 

2) Measure the Breadth: Measure the shorter side of the rectangle. Suppose this side is 5 metres; then this is your breadth. 

3) Apply the Formula: Multiply the length by the breadth. 

Example: If the length is 10 metres and the breadth is 5 metres: 

 This result tells us that the rectangle covers 50 square metres of area.

Continue learning with our easy-to-follow geometry guides on the Area of Rhombus. Click here for more educational content! 

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Area of a Rectangle using Diagonal 

Sometimes, you might not have direct measurements of the length and breadth, but you can measure the diagonal. The diagonal of a rectangle divides it into two right-angled triangles. By applying the Pythagorean theorem, you can relate the diagonal to the length and breadth. Similarly, understanding the Area of Isosceles Triangle helps in calculating areas when you know the base and height, as it involves applying basic geometric principles to find the area of symmetrical shapes.

 If you know the diagonal and either the length or breadth, you can use the Pythagorean theorem to find the missing dimension. Once both dimensions are known, you can calculate the area using the standard formula. 

 Example: If the diagonal is 13 metres and the length is 12 metres 

 Now, calculate the area: 

Area of a Rectangle using Perimeter 

The perimeter of a rectangle is the total length around it, while the area is the space inside. If you know the perimeter and one side length, you can find the area using these steps:

1) Use the perimeter formula:
 

Where P is the perimeter, L is the length, and B is the Breadth

2) Find the missing side:

3) Calculate the area:

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Why Area of the Rectangle is Length x Breadth? 

The reason the Area of a Rectangle is calculated by multiplying its length by its breadth lies in the way area is defined using square units. Imagine a rectangle divided into unit squares (each with an area of 1 square unit). Similarly, in circular shapes, the concept of area extends to sections like the Area of Quadrant, where the area is a fraction of the circle based on its radius.

The length tells you how many units fit along one side, and the breadth tells you how many units fit along the adjacent side. The total number of squares filling the rectangle (i.e., the area) is the product of these two numbers. 

This multiplication reflects the fact that area is a two-dimensional measurement, requiring both dimensions (length and breadth) to be considered.  

It also aligns with the distributive property in arithmetic, where multiplying two numbers gives the total count of units in a grid—in this case, the grid formed by the rectangle. Similarly, the Area of Trapezium involves calculating the total area within a defined shape, following a straightforward formula that reflects the relationship between its parallel sides and height.

Area of Rectangle: Solved Examples 

Let's look at some examples to solidify our understanding. 

Example 1  

A rectangle has a length of 15 metres and a breadth of 8 metres. Find the area. 

Solution: 

Example 2 

The perimeter of a rectangle is 40 metres, and its length is 12 metres. Find the area. 

Solution: 

First, find the breadth using the perimeter:  

 Now, calculate the area:  

Example 3 

A rectangle has a diagonal of 10 metres and a length of 6 metres. Find the area. 

Solution: 

Use the Pythagorean theorem to find the breadth:  

 Calculate the Area: 

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What is the Perimeter of a Rectangle?

The perimeter of a two-dimensional shape is the total length of its outline. For a rectangle, it is the sum of all four sides. Since opposite sides are equal, we use the formula:

Perimeter = 2 × (Length + Width). It is a linear measure with units like meters, centimetres, inches, or feet.

Conclusion 

Understanding the Area of a Rectangle is fundamental in both geometry and real-world applications. Whether you’re designing a space, calculating materials, or solving mathematical problems, the formula Area = Length x Breadth is an essential tool. This knowledge is versatile and widely applicable, extending to different shapes like the Area of a Square, which follows its own simple calculation method.

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