Area of Rectangle: Formula, Examples and Questions

Area of Rectangle is the region covered by a rectangle. For a rectangle with length l and breadth b, its area is l × b square units. This page explains the formula, unit rules, reverse calculations, scaling effects and solved area of rectangle problems for quantitative aptitude.

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What Is the Area of a Rectangle?

The area of a rectangle is the total surface enclosed by its four sides. It is calculated by multiplying its length by its breadth: Area = length × breadth.

If the length is l units and the breadth is b units, then area = l × b square units. The two dimensions must be expressed in the same unit before multiplication. For example, a rectangle measuring 12 cm by 5 cm has area 12 × 5 = 60 cm².

Area of Rectangle Video Lessons

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Rectangle Area and Perimeter

Learn how to calculate the area and perimeter of a rectangle using the standard formulas, with clear application of length and breadth measurements.

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Area of Rectangle Formula & Tricks

Important Formulas

Area of a rectangle
A = l × b

Here, A is the area, l is the length and b is the breadth. The answer is written in square units.

Length from area and breadth
l = A ÷ b

When the area and breadth are known, divide the area by the breadth to find the length.

Breadth from area and length
b = A ÷ l

When the area and length are known, divide the area by the length to find the breadth.

Area after changing dimensions
New area = (new length) × (new breadth)

Recalculate both dimensions after any increase or decrease. If length changes by a factor of x and breadth by a factor of y, the area changes by a factor of xy.

Quick Tricks

Convert units before multiplying

Length and breadth must use the same unit. The resulting area uses the square of that unit.

Example: For 2 m × 50 cm, convert 2 m to 200 cm. Area = 200 × 50 = 10,000 cm², or 2 × 0.5 = 1 m².
Use factors for percentage changes

If length increases by r% and breadth increases by s%, multiply the original area by (1 + r/100)(1 + s/100).

Example: If both dimensions increase by 10%, new area = original area × 1.1 × 1.1 = 1.21 times the original area, so the increase is 21%.

Area of Rectangle Concepts

Applying the Area Formula

Multiply the rectangle's length and breadth after expressing both measurements in the same unit.

The formula is A = l × b. A rectangle with length 18 m and breadth 7 m has area 18 × 7 = 126 m². Area is always measured in square units, not linear units.

Example: For l = 24 cm and b = 9 cm, A = 24 × 9 = 216 cm².

Unit Conversion for Rectangular Area

Convert each dimension to one unit before calculating the area.

Useful relations are 1 m = 100 cm, 1 m² = 10,000 cm², and 1 km² = 1,000,000 m². The conversion factor is squared because area has two dimensions.

Example: A rectangle measuring 3 m by 40 cm has area 300 cm × 40 cm = 12,000 cm², which is 1.2 m².

Finding a Missing Dimension

Divide the given area by the known dimension to find the missing dimension.

From A = l × b, length = A ÷ b and breadth = A ÷ l. If the area is 360 cm² and the length is 24 cm, the breadth is 360 ÷ 24 = 15 cm.

Example: If A = 540 m² and b = 18 m, then l = 540 ÷ 18 = 30 m.

Effect of Dimension Changes

The area changes by the product of the factors by which the length and breadth change.

If length becomes x times and breadth becomes y times, the new area is xy times the original area. If only the length doubles, the area doubles. If both length and breadth double, the area becomes four times the original.

Example: A rectangle of area 80 cm² has both dimensions increased by 50%. New area = 80 × 1.5 × 1.5 = 180 cm².

Area of Rectangle Visual Guide

Use the diagram or chart below to understand the concept clearly.

Rectangle with length and breadth

Visual guide: Rectangle with length and breadth
Length (l): 12 cm Breadth (b): 5 cm Area (l × b): 60 cm²
The area of the rectangle is the product of its length and breadth.

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Practice Area of Rectangle Questions

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1Find the HCF of the numbers 2520, 3600, 5880.→ 2A trader lost 10% by selling a shirt for ₹900. If he gains x% by selling it for ₹1,500, the value of x is:→ 3A shopkeeper gives 0.75 meter of cloth per customer. If he has 15 meters, how many customers can he serve completely?→ 4In what ratio should sugar costing ₹34/kg be mixed with sugar costing ₹58/kg so that by selling the mixture at ₹52.80/kg, there is a profit of 32%?→ 5Which of the following is smaller than (13/18)?→ 6Which of the following numbers is divisible by 7?→ 7A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more sugar for Rs. 240. What is the original price per kg of sugar?→ 8An article marked at ₹1,250 is sold at two successive discounts such that the selling price becomes ₹900. If the first discount is 20%, what is the second discount?→ 9If 20% of a number is added to 90, then the result is the same number. 60% of the same number is:→ 10Three years ago, the population of a town was 65,000. If the annual increase during three successive years occurs at the rate of 10%, 8% and 5%, respectively, what is its present population?→

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Quick Revision Notes

Area of Rectangle Revision Points

Recall the formula, unit rules and reverse methods for rectangular areas.

  • Area = length × breadth.
  • Length and breadth must be in the same unit before multiplication.
  • Area is expressed in square units such as cm², m² or km².
  • 1 m² = 10,000 cm² and 1 km² = 1,000,000 m².
  • Length = area ÷ breadth; breadth = area ÷ length.
  • If both dimensions are multiplied by k, the area is multiplied by k².
  • For a square, area = side² because its length and breadth are equal.

Related Topic Explainers

Area of Square → Perimeter of Square →

Area of Rectangle FAQs

What is the area of a rectangle with length 15 cm and breadth 8 cm?

Area = 15 × 8 = 120 cm².

What is the breadth of a rectangle with area 480 m² and length 24 m?

Breadth = area ÷ length = 480 ÷ 24 = 20 m.

How do you convert rectangular area from m² to cm²?

Multiply by 10,000 because 1 m² = 10,000 cm². Thus, 2.5 m² = 25,000 cm².

If the length of a rectangle increases by 20% and its breadth remains unchanged, how does its area change?

The area also increases by 20%, because area is directly proportional to length when breadth is constant.

If both dimensions of a rectangle decrease by 10%, what is the percentage decrease in area?

New area = 0.9 × 0.9 = 0.81 of the original area. Therefore, the area decreases by 19%.

What is the difference between the area and perimeter of a rectangle?

Area measures the enclosed surface and is l × b square units. Perimeter measures the boundary and is 2(l + b) linear units.

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