What is the area of a rectangle formula and how to calculate it
Do you have a book or a laptop in front of you? Notice its shape! It’s a rectangle. Do you see all four sides to be equal? No, right? A rectangle has two sides, length (L) and Breadth (B). The length of a rectangle is the longest side, whereas the range is the shortest side. The range of a rectangle is occasionally pertained to as the breadth (b).
Length and breadth are the tools that are used to find the confines of an object. When we relate to two-dimensional shapes (2D shapes), we use length and breadth. Continue reading to know more about rectangles.
What are Length and Width?
Before we proceed further, let us first understand what the following two terms mean.
Length: Length is used to scale the distance between two points. It is the lengthy size of a figure, and it shows how long the given object or figure is. It's expressed in direct units like measures, centimetres, elevation, etc.
Width: Width is the shorter length of an object or a figure, and it shows how broad or wide the given figure is. The range is also expressed in direct units like measures, centimetres, elevation, etc.
Length and Width
Area of a Rectangle
In the below figure, the area of the rectangle is the region covered by the rectangle in a two-dimensional plane. A rectangle is a quadrilateral, a 2-D shape with four sides and four vertices. All four sides of the rectangle are right sides or equal to 90 degrees. The opposite sides of the rectangle are equal and resemblant to each other. When observed, a parallelogram also has its opposite sides equal and resemblant to each other, but the angles aren't equal to 90 degrees.
Rectangle
What is the Area of a Rectangle?
The area of a rectangle is the region covered by a rectangle within its four sides or boundaries. The region of a rectangle depends on its sides. Principally, the formula for area is equal to the product of the length and breadth of the rectangle. However, when we speak about the border of a rectangle, it's equal to the sum of all its four sides. Hence, the region enclosed by the rectangle's border is its area.
Area of rectangle = Length x Breadth
A = l x b
Area of Rectangle Formula
The formula to find the area of a rectangle depends on its length and range. The area of a rectangle is calculated in units by multiplying the range (or breadth) by the Length of a rectangle. Side and total face areas can be calculated only for three-dimensional figures. We cannot calculate the rectangle since it's a two-dimensional figure. Therefore, the border and the area of a rectangle are given by:
The formula for the area of a rectangle is as follows:
A = l × b
Area of Rectangle Units
The area of a rectangle can be calculated by numbering the piece of small full places of measurement 1 * 1sq. units needed to fill in the rectangle.
When multiplying the length by the range, always ensure you work in the same unit of length. However, modify them to the same unit if given in different units.
Steps to Find the Area of a Rectangle
Follow the steps given below to determine the area of a rectangle:
Step 1: Note the values of length and range from the given data.
Step 2: Multiply length and range values.
Step 3: Write the results in square units.
Length and Breadth Formula
Length Formula
When we want to detect the length of a rectangle, we require to divide the area by breadth.
Length = Area ÷ breadth
ℓ = A ÷ b
The introductory formula for risking the length of a rectangle when we're contributing the breadth and area is only to divide the area by breadth.
Breadth Formula
When we want to find the breadth of a rectangle, we require to divide the area by length.
Breadth = Area ÷ length
b = A ÷ l
The primary formula for risking the breadth of a rectangle when we've presented the length and area is to only divide the area by length.
Solved Examples
Q 1. Find the area of a rectangle whose width is 20 cm and length is 4 cm.
Ans: Given, width = 20 cm and length = 4 cm
Area = w × l
Area = 20 × 4
thus, the area of the rectangle = 80 cm2.
Find the area of the rectangle whose length is 15 cm and the range is 4 cm.
result
Given,
Length = 15 cm
Range = 4 cm
Area of a rectangle = Length × range
15 × 4 = 60
Hence, the area of the rectangle = 60 cm2
Q 2. The length of a blockish screen is 15 cm. Its area is 180sq. cm. Find its width.
Ans: Area of the screen = 180 sq. cm.
Length of the screen = 15 cm
Area of a rectangle = length x range
So, width = area/ length
Therefore, width of the screen = 180/15 = 12 cm
Practice Questions
Q 1. Find the area of a rectangle whose width is 10 cm and length is 2 cm.
Ans: 20 cm2
Q 2. Find the area of a rectangle whose width is 30 cm and length is 4 cm.
Ans: 120 cm2
Summary
A rectangle is a four-sided shape with two pairs of parallel sides. It is the most basic shape which has many uses in Maths and everyday life. A rectangle is characterised by length (L) and width/ breadth (W). Both length and width are different in size. The area is the region covered by a two-dimensional shape in a plane. It's measured in square units. Thus, the area of the rectangle is the region enclosed by its external boundaries. It's equal to the product of length and width.
FAQs on Area of Rectangle Complete Concept Guide
1. What is the formula for the area of a rectangle?
The formula for the area of a rectangle is Area = length × width (A = l × w).
- Measure the length of the rectangle.
- Measure the width (breadth).
- Multiply both values to get the area in square units.
2. How do you calculate the area of a rectangle step by step?
To calculate the area of a rectangle, multiply its length by its width.
- Step 1: Identify the length (l).
- Step 2: Identify the width (w).
- Step 3: Use the formula A = l × w.
- Step 4: Write the answer in square units.
3. Why is the area of a rectangle length times width?
The area of a rectangle is length × width because it counts the total number of square units that fit inside it.
- A rectangle can be divided into rows and columns of equal squares.
- The number of squares in one row equals the length.
- The number of rows equals the width.
- Total squares = length × width.
4. What are the units for the area of a rectangle?
The area of a rectangle is measured in square units such as cm², m², or in².
- If length and width are in centimeters, area is in cm².
- If they are in meters, area is in m².
- If they are in inches, area is in in².
5. What is the difference between area and perimeter of a rectangle?
The area of a rectangle measures the space inside it, while the perimeter measures the distance around it.
- Area formula: A = l × w
- Perimeter formula: P = 2(l + w)
- Area = 6 × 4 = 24 cm²
- Perimeter = 2(6 + 4) = 20 cm
6. Can you give an example of finding the area of a rectangle?
Yes, you can find the area by multiplying the given length and width.
- Given: length = 9 m, width = 7 m
- Formula: A = l × w
- Calculation: 9 × 7 = 63
7. How do you find the area of a rectangle if only one side and the perimeter are given?
You can find the missing side using the perimeter formula and then apply A = l × w.
- Use P = 2(l + w) to find the unknown side.
- Substitute the known values and solve.
- Multiply length and width to get the area.
- 30 = 2(10 + w)
- 15 = 10 + w → w = 5 cm
- Area = 10 × 5 = 50 cm²
8. What happens to the area of a rectangle if the length is doubled?
If the length of a rectangle is doubled while width stays the same, the area also doubles.
- Original area = l × w
- New area = (2l) × w = 2lw
9. Is the area of a square calculated the same way as a rectangle?
Yes, a square’s area is calculated similarly because it is a special rectangle with equal sides.
- Rectangle formula: A = l × w
- Square formula: A = side × side = s²
10. What are common mistakes when finding the area of a rectangle?
Common mistakes include using the wrong formula or forgetting square units.
- Confusing area with perimeter.
- Adding instead of multiplying length and width.
- Not writing the answer in square units (e.g., cm², m²).
- Using different units without converting them first.
