Mensuration

About 6 min · Mathematics · English

Time worked out from the lesson's 396 words at 150 words a minute, plus a minute for each question.

It deals with the measurement of geometric figures: finding area, perimeter, surface area, and volume of 2-D and 3-D shapes. This topic is formula-intensive and many questions are direct applications once you know the right formula.

Key ideas

Perimeter is the total boundary length of a 2-D figure; measured in linear units (cm, m). Used for fencing, framing, or bordering problems.
Area is the surface enclosed by a 2-D figure; measured in square units (cm², m²). Common in flooring, painting, and land measurement problems.
Surface Area is the total outer area of a 3-D object; measured in square units. Two types: Lateral Surface Area (LSA) excludes top/bottom; Total Surface Area (TSA) includes all faces.
Volume is the space occupied by a 3-D object; measured in cubic units (cm³, m³, liters). Used in tank capacity, material quantity, and liquid problems.
Composite Figures combine two or more basic shapes. Break them into recognizable parts, calculate separately, then add or subtract as needed.

Watch out for

Mixing up LSA and TSA → Remember: LSA excludes top/bottom (e.g., for painting walls); TSA includes all surfaces (for covering entire object).
Forgetting to square or cube during conversion → 5 m = 500 cm is correct, but 5 m² ≠ 500 cm². It's 5 × 10,000 = 50,000 cm². Always square/cube the conversion factor.
Using diameter instead of radius → Formulas use radius (r). If diameter (d) is given, first find r = d/2 before substituting.

Quick reference

Rectangle area = l × b; Square area = a²; Circle area = πr²
Cube volume = a³; Cuboid volume = l × b × h; Cylinder volume = πr²h
Cone volume = ⅓πr²h; Sphere volume = (4/3)πr³
Total surface area includes all faces; Lateral surface area excludes top/bottom
Always convert units before calculation; 1 m² = 10,000 cm²; 1 m³ = 1,000,000 cm³

Check yourself: 3 questions

1. A rectangular field is 60 metres long and 40 metres wide. What is the cost of fencing it at the rate of Rs. 15 per metre?
2. A circular garden has a radius of 21 metres. Find the area of the garden. (Use π = 22/7)
3. A cubical water tank has an edge of 5 metres. How many litres of water can it hold? (1 cubic metre = 1,000 litres)

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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