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Physical Quantities and Measurement - Measurement of Area

Grade 6ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Area is defined as the measure of the surface occupied by a plane figure or a closed shape.

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The standard SI unit of area is the square metre, denoted as m2m^2. One m2m^2 is the area of a square with each side measuring 1 m1\text{ m}.

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For measuring small areas, units like square centimetre (cm2cm^2) and square millimetre (mm2mm^2) are used. Relationship: 1 cm2=100 mm21\text{ cm}^2 = 100\text{ mm}^2 and 1 m2=10,000 cm21\text{ m}^2 = 10,000\text{ cm}^2.

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Large land areas are measured in units like Are and Hectare. 1 Are=100 m21\text{ Are} = 100\text{ m}^2 and 1 Hectare=100 Ares=10,000 m21\text{ Hectare} = 100\text{ Ares} = 10,000\text{ m}^2.

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The area of irregular surfaces (like a leaf) can be estimated using a centimeter graph paper by counting the number of squares enclosed within the boundary.

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When using graph paper: count full squares as 11, squares more than half filled as 11, squares exactly half filled as 0.50.5, and ignore squares less than half filled.

📐Formulae

Area of a Rectangle=length (l)×breadth (b)Area\ of\ a\ Rectangle = length\ (l) \times breadth\ (b) pieces

Area of a Square=side (s)×side (s)=s2Area\ of\ a\ Square = side\ (s) \times side\ (s) = s^2

1 m2=10,000 cm21\text{ m}^2 = 10,000\text{ cm}^2

1 hectare=10,000 m21\text{ hectare} = 10,000\text{ m}^2

1 km2=1,000,000 m21\text{ km}^2 = 1,000,000\text{ m}^2

💡Examples

Problem 1:

Calculate the area of a rectangular table top whose length is 2.5 m2.5\text{ m} and breadth is 1.2 m1.2\text{ m}.

Solution:

Given: l=2.5 ml = 2.5\text{ m}, b=1.2 mb = 1.2\text{ m}. Using the formula Area=l×bArea = l \times b, we get Area=2.5 m×1.2 m=3.0 m2Area = 2.5\text{ m} \times 1.2\text{ m} = 3.0\text{ m}^2.

Explanation:

To find the area of a rectangle, multiply the length by the breadth. Ensure both units are the same before multiplying.

Problem 2:

Find the area of a square field in hectares if its side measures 200 m200\text{ m}.

Solution:

Area=s×s=200 m×200 m=40,000 m2Area = s \times s = 200\text{ m} \times 200\text{ m} = 40,000\text{ m}^2. Since 1 hectare=10,000 m21\text{ hectare} = 10,000\text{ m}^2, Area=40,00010,000=4 hectaresArea = \frac{40,000}{10,000} = 4\text{ hectares}.

Explanation:

First, calculate the area in m2m^2 by squaring the side, then convert to hectares by dividing by 10,00010,000.

Problem 3:

A leaf occupies 1515 full squares and 88 more-than-half squares on a graph paper where each square is 1 cm21\text{ cm}^2. What is its approximate area?

Solution:

Total squares=15+8=23Total\ squares = 15 + 8 = 23. Since each square is 1 cm21\text{ cm}^2, Area≈23×1 cm2=23 cm2Area \approx 23 \times 1\text{ cm}^2 = 23\text{ cm}^2.

Explanation:

For irregular shapes on graph paper, we sum the full and more-than-half squares to estimate the total surface area.

Measurement of Area - Revision Notes & Key Formulas | ICSE Class 6 Science