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Measurement - Measurement of Area

Grade 7ICSE

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

🔑Concepts

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Area is the measure of the surface covered by a closed plane figure. The standard SI unit of area is the square metre (m2m^2).

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Multiples of units are used for larger areas: 1 are=100 m21 \text{ are} = 100 \text{ m}^2 and 1 hectare=100 are=10,000 m21 \text{ hectare} = 100 \text{ are} = 10,000 \text{ m}^2.

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Sub-multiples are used for smaller areas: 1 cm2=10−4 m21 \text{ cm}^2 = 10^{-4} \text{ m}^2 and 1 mm2=10−6 m21 \text{ mm}^2 = 10^{-6} \text{ m}^2.

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For irregular shapes, a graph paper method is used. The total area is estimated by counting: (a) Full squares, (b) Squares more than half-filled as full, (c) Exactly half-filled squares as 0.50.5, and (d) Ignoring squares less than half-filled.

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The area of a composite figure is the sum of the areas of the individual regular geometric shapes that make it up.

📐Formulae

Area of a Square=side×side=s2\text{Area of a Square} = \text{side} \times \text{side} = s^2

Area of a Rectangle=length×breadth=l×b\text{Area of a Rectangle} = \text{length} \times \text{breadth} = l \times b

Area of a Triangle=12×base×height=12bh\text{Area of a Triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} bh

Area of a Circle=πr2 (where π≈227 or 3.14)\text{Area of a Circle} = \pi r^2 \text{ (where } \pi \approx \frac{22}{7} \text{ or } 3.14)

Area of a Parallelogram=base×height\text{Area of a Parallelogram} = \text{base} \times \text{height}

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

💡Examples

Problem 1:

A rectangular field has a length of 50 m50 \text{ m} and a breadth of 30 m30 \text{ m}. Calculate its area in hectares.

Solution:

Area=l×b=50 m×30 m=1500 m2\text{Area} = l \times b = 50 \text{ m} \times 30 \text{ m} = 1500 \text{ m}^2 Since 1 hectare=10,000 m21 \text{ hectare} = 10,000 \text{ m}^2, Area in hectares=150010000=0.15 hectares\text{Area in hectares} = \frac{1500}{10000} = 0.15 \text{ hectares}

Explanation:

First, calculate the area in square metres using the rectangle formula, then convert it to hectares by dividing by 10,00010,000.

Problem 2:

Find the area of a circular disc with a diameter of 14 cm14 \text{ cm}. (Use π=227\pi = \frac{22}{7})

Solution:

Radius (r)=diameter2=142=7 cm\text{Radius (r)} = \frac{\text{diameter}}{2} = \frac{14}{2} = 7 \text{ cm} Area=πr2=227×(7 cm)2\text{Area} = \pi r^2 = \frac{22}{7} \times (7 \text{ cm})^2 Area=227×49=22×7=154 cm2\text{Area} = \frac{22}{7} \times 49 = 22 \times 7 = 154 \text{ cm}^2

Explanation:

First find the radius by dividing the diameter by 22. Then apply the formula for the area of a circle.

Problem 3:

While measuring an irregular leaf on graph paper, a student counts 1212 complete squares, 88 squares that are more than half-filled, and 44 squares that are exactly half-filled. If each square is 1 cm21 \text{ cm}^2, what is the area?

Solution:

Total Area=(12×1)+(8×1)+(4×0.5)\text{Total Area} = (12 \times 1) + (8 \times 1) + (4 \times 0.5) Total Area=12+8+2=22 cm2\text{Total Area} = 12 + 8 + 2 = 22 \text{ cm}^2

Explanation:

The rule for irregular shapes on graph paper is to count full and more-than-half squares as 11, and half squares as 0.50.5.

Measurement of Area - Revision Notes & Key Formulas | ICSE Class 7 Science