Area of a Rectangle – Definition, Formula, Examples | How to find the Area of a Rectangle?

Students should have a good grip on all basic concepts of maths in primary school only as it helps them in further studies. Kids who are studying in 5th Standard should be particular about important topics like Shapes. It is the most fundamental concept in maths which should be practiced and understood by every kid. When we draw plane figures with their shape, region, and boundary, we obviously compare the objects with their size and area.

There are different geometrical shapes like squares, circles, and rectangles, etc. While solving geometrical problems, the area of a rectangle plays an important role. On this page, you will understand the concept of the area of a rectangle in detail along with steps to find Length or Breadth when the Area of a Rectangle is given.

Do Refer:

What is the Area of a Rectangle?

The area occupied by a rectangle within its boundary is called the Area of a Rectangle and it can be defined by its sides. It is measured in terms of the square units. The area of a rectangle is the region sheltered by the rectangle in a two-dimensional plane as the amount of space covered by a flat surface of a particular shape.

Few examples of a rectangle are planks, laptops, LEDs, and blackboards, etc. You can use the formula to find the size of these objects. Let us represent a rectangle how it looks.

Rectangle

Area of Rectangle Formula

The size of any object can be measured in different ways. To solve the problems related to the area of the rectangle easily, children should be aware of the area of the rectangle formula.

The formula of the area of a rectangle is calculated in units by multiplying the length and width of the rectangle given.

Area of a Rectangle = Length × Width square units (i.e., A = l×w sq units).

Where a rectangle is of two sides. The length of a rectangle is the largest side and the width is the smallest side. The width of a rectangle is sometimes referred to as breadth(b). Square units may be square centimeters, square inches, etc.

The area of any rectangle is calculated if the length and width of the size are known. By multiplying both the length and the width, the area of a rectangle is measured and it is represented in square units.

Total surface areas can be multiplied or calculated only if the shapes are three-dimensional figures. We cannot calculate for the rectangle because they are two-dimensional figures.

Perimeter of a rectangle = 2(length + breadth)  (i.e., P = 2(l+b)).

How to Calculate the Area of a Rectangle?

To find the area of a rectangle, students should know the length and width of a rectangle and it will be easy to multiply and get the area of a rectangle in square units. Let us follow some simple steps to calculate the area of a rectangle.

Step 1: Observe the rectangle and write the dimensions of length and width from the given data.
Step 2: Now, apply the area of a rectangle formula, a = l×w.
Step 3: Write the obtained answer in square units.

Area of a Rectangle by Diagonal

There are two diagonals in a rectangle and both are of equal length. The straight line connecting is opposite vertices is the diagonal of a rectangle. The formula we use to find the diagonal of a rectangle is as follows.

(Diagonal)² = (length)² + (breadth)²

From this,

(length)² = (diagonal)² – (breadth)²
length = √(diagonal)² – (breadth)²

(breadth)² = (diagonal)² – (length)²
breadth = √(diagonal)² – (length)²

Now, the area of a rectangle = length × breadth

Area = length × (√(diagonal)² – (length)²)

Area of a Rectangle Examples

Example 1: 
Find the area of the rectangle whose length is 14 cm and the width is 6 cm.
Solution: 
Given
length 14 cm, width 6 cm
Area of a rectangle = length × width
A = 14 × 6 = 84 sq cm.
Thus, the area of a rectangle is 84 square centimeters.

Example 2: 
The length and width of a rectangular field are 100 yards and 70 yards. Find the area of the field.
Solution:
Given
Length of the field = 100 yards
Width of the field = 70 yards
Area of the field = length of the field × width of the field
A = 100 × 70 = 700 sq yards.
Hence, the area of the field is 700 square yards.

Example 3: 
Find the area of the tennis court whose length and breadth are 55 m and 25 m respectively.
Solution: 
Given
The length of the tennis court is 55m.
The Width of the tennis court is 25m.
Area of the tennis court = length × width
A = 55m × 25m = 1375 sq mts.
Therefore, the area of the tennis court is 1375 square meters.

Example 4: 
The area of a rectangle is 36 cm². If its breadth is 8 cm then find its length?
Solution: 
Given, Area of a rectangle is 36 sq cm and the Breadth is 8 cm.
Formula for area of a rectangle = length × width
Now, to find the length
Length = Area of a rectangle / Width
Length = 48 sq cm / 8 cm = 8cm
Hence, the length of a rectangle is 8 cm.

FAQs on Area of Rectangle

1. What is the area and perimeter of a rectangle?
The perimeter of a rectangle is the addition of its four sides. Thus, Perimeter of a rectangle = 2 (length + width) units. The area of a rectangle is defined as the multiplication of length and width of a rectangle. Thus, the area of a rectangle = length × width square units.

2. What is the unit area of a rectangle?
The unit of area of a rectangle is a ‘square unit’. For example, if the dimensions of a rectangle are 3 inches × 2 inches then the area of a rectangle is 6 square inches.

3. Why do we compute the area of a rectangle?
We compute the area of a rectangle to find the area occupied by a rectangle within its perimeter.

4. Is the area of a square and area of a rectangle are same?
No, the area of a rectangle and the area of a square is different because every square is a rectangle with its length and breadth but all the rectangles are not squares. The area of a rectangle is measured in square units whereas square is measured by (side)².

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