Area of the Rectangle is the region covered inside the boundaries of the rectangle. The area of a rectangle is calculated using its dimensions length and breadth similar to the square in which the side is both the length and breadth.
To find the area, you multiply the length of the rectangle by its width., the formula for the Area of the Rectangle,
A = l x b, where l and b are the length and breadth of the rectangle.
In this article, we are going to study about area of the rectangle in detail, including its formula and examples.
Properties of Rectangle
Some of the common properties of rectangles are:
| Property | Description |
|---|
| Shape | Symmetrical and regular |
| Angles | All angles are 90° (right angles) |
| Opposite Sides | Equal in length |
| Diagonals | Bisect each other at right angles and are of equal length |
Area of RectangleThe area of rectangle is the product of length (L) and breadth (B).
Area of rectangle Formula, A = L x B
Where,
- L is the length of the rectangle,
- B is the breadth of the rectangle
Note: If the unit of length and breadth is not exact then it should be transformed into one unit. For e.g. If the length is in cm and breadth in m then both dimensions should be adjusted either to m or cm.
Unit of Area of Rectangle
The area of a rectangle is measured in square units and the standard unit for measuring the area of a rectangle is m2. Other units widely used for measuring the area of the rectangle are cm2, mm2, and others.
Side | Area |
|---|
| meter(m) | m2 or (meter)2 |
| centimeter(cm) | cm2 or (centimeter)2 |
How to Find Area of Rectangle?
The area of the rectangle is defined as the product of its length and breadth. Following are the steps that help calculate the area of the rectangle,
Step 1: Note down the dimensions of the rectangle.
Step 2: Calculate the product of the length and breadth of the rectangle.
Step 3: Write the answer in respective square units.
Example: Find the area of a rectangle whose length is 20 inches and breadth is 50 inches.
Solution:
The formula for area of rectangle is given:
Area = L × B
⇒ Area = 20 × 50
⇒ Area = 1000 inches2
Thus, the required area is 1000 inches2
Area of rectangle is the product of length and breadth. This can be derived by dividing the rectangle into two triangles. The triangles are equal as the base and height of the two triangles will be equal.
Let's derive the formula for the area of rectangle, the image given below shows that a rectangle is made by joining two equal right-angle triangles.
Area of a Rectangle Formula DerivationArea of Rectangle = 2 (Area of Triangle)
⇒ Area of Rectangle = 2 (1/2 × Base × Height)
⇒ Area of Rectangle = 2 (1/2 × AB × BC)
⇒ Area of Rectangle = AB × BC
⇒ Area of Rectangle = Length × Breadth.
Thus, the area of rectangle formula is derived.
Area of Rectangle using Diagonal
The area of the rectangle can be found by two methods which are:
Method 1 ( Using Diagonal and One Side of Rectangle)
We can find the value of the missing side using the Pythagoras theorem and then find the area. Let us understand this using an example.
The diagonal of the rectangle is the line joining opposite vertices. The diagonal of the rectangle is calculated using Pythagoras's Theorem
Area of Rectangle Using the Diagonals(Diagonal)2 = (Length)2 + (Breadth)2
⇒ Length2 = (Diagonals2 - Breadth2)
⇒ Length = √(Diagonals2 - Breadth2)
The formula for the area of a rectangle is calculated by:
Area = Length × Breadth
⇒ Area = √(Diagonals2 - Breadth2) × Breadth
⇒ Area = Breadth √(Diagonals2 - Breadth2)
Method 2 (Using Area of Quadrilateral Formula)
If both the diagonals of the rectangle are given then its area can be found with the help of the area of the quadrilateral formula.
Let a rectangle ABCD have diagonals as AC and BD and their length is d1 and d2 then its area is given by,
Area of rectangle ABCD = 1/2 × d1 × d2
Example: Find the area of a rectangle whose length of the diagonals is 10 cm and 14 cm.
Solution:
The formula for area of rectangle is,
Area = 1/2 × d1 × d2
⇒ Area = 1/2 × 10 × 14
⇒ Area = 70 cm2
Thus, the area of required rectangle is 70 cm2.
Area of Rectangle Using Perimeter
Follow the following steps, to calculate the area of a rectangle using the perimeter and one side of the rectangle:
- Step 1: Note the perimeter and the given dimension.
- Step 2: Use the perimeter formula to find the other dimension.
- Step 3: Use the area of the rectangle formula and substitute the required value obtained in Step 2
- Step 4: Simplify the expression and add unit2 to get the final answer.
The example given below explains the above concept.
Example: Find the area of a rectangle when the perimeter is 28 cm and the breadth is 8 cm.
Solution:
Given,
Perimeter of Rectangle = 28 cm
length = 8 cm
breadth(b) = ?
Using Perimeter of rectangle formula,
Perimeter of rectangle = 2 (l + b)
⇒ 28 = 2 (8 + b)
⇒ 14 = 8 + b
⇒ b = 6 cm
Thus the breadth of rectangle is 6 cm
Area of Rectangle = l × b
⇒ Area of Rectangle = 8 × 6 = 48 cm2
Thus, the area of the Rectangle is 48 cm2
Articles related to Area of Rectangle:
Area of Rectangle Examples
Example 1: The length and width of a rectangle are 6 units and 3 units, respectively. Find the area of rectangle.
Solution:
Given,
- length = 6 units
- breadth = 3 units
Area of rectangle = length × breath
⇒ Area of rectangle = 6 × 3
⇒ Area of rectangle = 18 square units
Thus, the area of given rectangle is 18 square units
Example 2: The height of a rectangular net is seen to be 20 cm. Its area is seen to be 260 cm2. Find the width of the provided net.
Solution:
Given,
Height = 20 cm
Area = 260 cm2
Area of Rectangle = width × height
⇒ width = Area / height
⇒ width = 260/20
⇒ width = 13 cm
Thus, the width of the rectangle is 13 cm
Example 3: The height and width of a rectangular desk are 40 m and 20 m, respectively. If a carpenter charges ₹ 2 per m2 for his work, how much would it cost to make the whole desk?
Solution:
Given,
Height of Desk = 40 m
Width of Desk = 20 m
Area of top of Desk = width of desk × height of desk
⇒ Area of top of Desk = 40 × 20
⇒ Area of top of Desk = 800 m2
At the cost of ₹ 2 per m2,
The cost for making top of the desk is 800 × 2 = ₹ 1600
Example 4: A wall whose length and width are 60 m and 40 m respectively needs to be painted. Find the quantity of the paint required if 1 litre of paint can paint 400 m2 of the wall.
Solution:
Given,
Length of wall = 60 m
Width of wall = 40 m
Thus, Area of wall = width × length
⇒ Area of wall = 60 × 40
⇒ Area of wall = 2400 m2
Paint required for 400 m2 of wall = 1 litre (given)
⇒ Paint required for 2400 m2 of wall = 2400 / 400 × 1 = 6 litre.
Thus, the paint required to paint the wall is 6 litre.
Area of Rectangle Worksheet
Question 1: What is the area of a Rectangular Field of length 15 m and width 8 m.
Question 2: Find the Area of a Rectangle whose length is twice its breadth and perimeter is 72 cm.
Question 3: What is the cost of tiling a floor of length 10 m and with 11 m at the rate of 15 rupees per square metre?
Question 4: How many boxes of dimension 10 cm by 9 cm can be placed on a floor of 10m by 9 m.
Using Diagonal and One side
Question 1: The diagonal of a rectangle is 13 cm, and one of its sides is 5 cm. Use the Pythagorean theorem to find the area of the rectangle.
Question 2: A rectangle has a diagonal of 17 cm and one side of 8 cm. Find the area of the rectangle.
Question 1: Find the area of rectangle that has two diagonals, each measuring 20 cm.
Question 2: Calculate the area of rectangle whjose diagonal measure 34 cm each.
Conclusion
This article provides a comprehensive overview of the area of a rectangle, covering its definition, properties, formula, derivation, methods of calculation, and examples. It includes explanations of how to find the area using the length and width, diagonals, perimeter, and real-life applications. Additionally, it offers practice questions and a summary for quick reference.
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