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What is the Area Formula for a Rectangle (l × b)?
Grade Level:
Class 3
Geometry, Engineering, Computing, AI
Definition
What is it?
The area formula for a rectangle (l × b) helps us find out how much flat space a rectangle covers. 'l' stands for the length (how long it is) and 'b' stands for the breadth or width (how wide it is). We multiply these two measurements to get the area.
Simple Example
Quick Example
Imagine your school's cricket pitch is a rectangle. If the pitch is 20 meters long and 5 meters wide, its area would be 20 meters × 5 meters = 100 square meters. This tells you the total ground space it occupies.
Worked Example
Step-by-Step
PROBLEM: A rectangular study table has a length of 120 cm and a breadth of 60 cm. What is its area?
STEP 1: Identify the given values.
Length (l) = 120 cm
Breadth (b) = 60 cm
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STEP 2: Recall the formula for the area of a rectangle.
Area = Length × Breadth (l × b)
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STEP 3: Substitute the values into the formula.
Area = 120 cm × 60 cm
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STEP 4: Perform the multiplication.
Area = 7200 square cm
ANSWER: The area of the study table is 7200 square cm.
Why It Matters
Understanding area is crucial in fields like engineering to design buildings and roads efficiently. In computing and AI, it helps with image processing and understanding space. Architects, city planners, and even game developers use this concept daily.
Common Mistakes
MISTAKE: Adding length and breadth instead of multiplying them. | CORRECTION: Always multiply the length and breadth to find the area. Addition gives you the perimeter, not the area.
MISTAKE: Forgetting to write the units as 'square units' (e.g., cm instead of sq cm). | CORRECTION: Area is always measured in square units (like square meters, square feet, square cm) because it's a 2D measurement.
MISTAKE: Mixing up length and breadth if they are given in different units. | CORRECTION: Ensure both length and breadth are in the same units before multiplying. If one is in meters and the other in cm, convert one to match the other.
Practice Questions
Try It Yourself
QUESTION: A rectangular photo frame is 30 cm long and 20 cm wide. What is the area of the photo it can hold? | ANSWER: 600 square cm
QUESTION: A rectangular garden plot measures 15 meters by 8 meters. How much area does it cover? | ANSWER: 120 square meters
QUESTION: A rectangular floor needs new tiles. The floor is 10 meters long and 6 meters wide. If each tile covers 1 square meter, how many tiles are needed? | ANSWER: 60 tiles
MCQ
Quick Quiz
What is the area of a rectangle with length 7 cm and breadth 4 cm?
11 sq cm
28 sq cm
22 cm
28 cm
The Correct Answer Is:
B
The area of a rectangle is found by multiplying length by breadth (l × b). So, 7 cm × 4 cm = 28 square cm. Options A and C are incorrect calculations, and option D uses the wrong units.
Real World Connection
In the Real World
When a civil engineer plans a new building in Mumbai, they use the area formula to calculate the floor space of each room or the total land required. Similarly, a farmer in Punjab uses it to figure out the size of their field for planting crops.
Key Vocabulary
Key Terms
AREA: The amount of surface covered by a 2D shape | RECTANGLE: A four-sided shape with four right angles | LENGTH: The measurement of how long something is | BREADTH: The measurement of how wide something is (also called width) | SQUARE UNITS: The units used to measure area, like square meters or square cm
What's Next
What to Learn Next
Great job understanding the area of a rectangle! Next, you can explore how to find the area of other shapes like squares and triangles. This will help you measure more complex spaces around you.
