Area of Rectangle
The area of any shape is the number of unit squares that can fit into it. Here "unit" refers to one (1) and a unit square is a square with a side of 1 unit. So, the area of a rectangle is the number of unit squares within the boundary of the rectangle. Alternatively, the space occupied within the perimeter of a rectangle is called the area of the rectangle. One good example of a rectangle shape is the square tiles of unit length in your house. You can easily figure out how much space the floor occupies by counting the number of tiles. This will also help you determine the area of the rectangular floor.
| 1. | What is Area of a Rectangle? |
| 2. | Area of a Rectangle Formula |
| 3. | Calculation of Area of Rectangle |
| 4. | Area of a Rectangle by Diagonal |
| 5. | Why Area of a Rectangle is Length × Breadth? |
| 6. | FAQs |
What is Area of a Rectangle?
The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle. Some examples of rectangular shapes are the flat surfaces of laptop monitors, blackboards, painting canvas, etc. You can use the formula of the area of a rectangle to find the space occupied by these objects. For example, let us consider a rectangle of length 4 inches and width 3 inches.
Area of a rectangle Definition: Area occupied by a rectangle within its boundary is called the area of the rectangle.
Let us draw unit squares inside the rectangle. Each unit square is a square of length 1 inch.
Now, count the number of unit squares in the above figure. How many squares can you observe? There are 12 squares in total. We have already learned that area is measured in square units. Since the unit of this rectangle is "inches," the area is measured and written in square inches. Thus, the Area of the above rectangle = 12 square inches.
Area of a Rectangle Formula
The formula of the area of a rectangle is used to find the area occupied by the rectangle within its boundary. In the above example, the area of the rectangle whose length is 4 inches and the width is 3 inches is 12 square inches. We have 4 × 3 = 12. The area of a rectangle is obtained by multiplying its length and width. Thus, the formula for the area, 'A' of a rectangle whose length and width are 'l' and 'w' respectively is the product "l × w".
Area of a Rectangle= (Length × Breadth) square units
Calculation of Area of Rectangle
The area of a rectangle is equal to its length times its width. Follow the steps mentioned below to find the area of a rectangle.
- Step 1: Note the dimensions of length and breadth from the given data.
- Step 2: Find the product of length and breadth values.
- Step 3: Give the answer in square units.
Let us take an example to understand the calculation of the area of a rectangle. We will find the area of the rectangle whose length is 15 units and breadth is 4 units. To find the area, first, find the length and width.
Given, length = 15 units and width = 4 units
The formula to find the area of a rectangle is A = l × w. Substitute 15 for 'l' and 4 for 'w' in this formula. Area of a rectangle = 15 × 4 = 60.
Therefore, the area of rectangle = 60 square units
Area of a Rectangle by Diagonal
The diagonal of a rectangle is the straight line in the rectangle connecting its opposite vertices. There are two diagonals in the rectangle and both are of equal length. We can find the diagonal of a rectangle by using the Pythagoras Theorem.
(Diagonal)2 = (Length)2 + (Breadth)2
(Length)2 = (Diagonal)2 - (Breadth)2
Length = ⎷ (Diagonal)2 - (Breadth)2
Now, the formula to calculate the area of a rectangle is Length × Breadth. Alternatively, we can write this product as (⎷ (Diagonal)2 - (Breadth)2)× Breadth
So, Area of a Rectangle = Breadth (⎷ (Diagonal)2 - (Breadth)2)
Why Area of a Rectangle Is Length × Breadth?
Have you ever wonder why the formula to find the area of a rectangle is Length × Breadth? Let's derive the formula of the area of a rectangle. We will draw a diagonal AC in the rectangle ABCD. Clearly, the diagonal AC divides the rectangle ABCD into two congruent triangles. The area of the rectangle is the sum of the area of these two triangles.
Area of Rectangle ABCD = Area of Triangle ABC + Area of Triangle ADC
= 2 × Area of Triangle ABC
= 2 × (1/2 × Base × Height)
= AB × BC
= Length × Breadth
Solved Examples on Area of Rectangle
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Example 1:
The length and width of a rectangular farm are 80 yards and 60 yards. Find the area of the farm.
Solution:
Length of the farm, l = 80 yd and width of the farm, w = 60 yards
Area of the farm A is: A = l × w
= 80 yd × 60 yards
= 4800 square yards
Therefore, the Area of the farm is 4800 square yards.
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Example 2:
Peter reads his favorite comic book in his study room. Can you find the area of the book whose length is \(3 \dfrac{1}{4} \) in. and width is \(1 \dfrac{1}{2}\) in?
Solution
Length of the book, l = \(3\dfrac{1}{4}\) inches
Width of the book, b = \(1\dfrac{1}{2}\) inches
Area of the rectangle A
A = l × b
= \(3 \dfrac{1}{4}\) × \(1 \dfrac{1}{2}\)
= 13/4 × 3/2= 39/8
= \(4\dfrac{7}{8}\) in2So, The area of book is \({4 \dfrac{7}{8}}\) square inches.
FAQs on Area of Rectangle
What is the Area of a Rectangle?
The area of the space occupied within the perimeter of a rectangle is called the area of a rectangle. It is calculated by finding the product of the length and breadth of the rectangle.
What is the Perimeter of a Rectangle?
The perimeter of a rectangle is the sum of its four sides. Hence, Perimeter of Rectangle = 2 (Length + Width) units.
What is the Formula for the Area of a Rectangle?
The area of a rectangle (A) is the product of its length 'a' and width 'b'. So, Area of Rectangle = (a × b) square units.
What is the Unit of Area of a Rectangle?
The unit of area of a rectangle is square units. For example, if the dimensions of a rectangle are 4 inches × 3 inches. The area of the rectangle is 12 square inches.
Why do we Calculate the Area of a Rectangle?
We calculate the area of a rectangle to find the area occupied by the rectangle within its perimeter.
How can we Find the Area of a Rectangle Using its Diagonal?
We can find the diagonal of a rectangle by using the Pythagoras Theorem: (Diagonal)2 = (Length)2 + (Breadth)2. Now, the formula to calculate the area of a rectangle is Length × Breadth. Alternatively, we can write this product as (⎷ (Diagonal)2 - (Breadth)2)× Breadth
Is the Area of the Rectangle the Same as the Area of the Square?
No, the area of the square is not necessarily the same as the area of the rectangle because every square is a rectangle with length and breadth equal but all rectangles are not square. The formula to calculate the area of rectangle is Length × Breadth and that of the square is (side)2.