Mensuration
About 6 min · Mathematics · English
Time worked out from the lesson's 400 words at 150 words a minute, plus a minute for each question.
Mensuration is the branch of mathematics dealing with the measurement of geometric figures—their lengths, areas, and volumes.
Key ideas
- Perimeter is the total length of the boundary of a 2D shape. Think of it as the distance you would walk if you traced the outline.
- Area measures the surface enclosed within a 2D boundary, expressed in square units (cm², m²).
- Surface Area of a 3D solid is the total area of all its outer faces. Distinguish between Curved Surface Area (CSA)—the curved part only—and Total Surface Area (TSA)—curved plus flat faces.
- Volume measures the space occupied by a 3D object, expressed in cubic units (cm³, m³). For liquids, 1000 cm³ = 1 litre.
- Unit Consistency: Always convert measurements to the same unit before calculating. Common conversions: 1 m = 100 cm; 1 km = 1000 m; 1 m² = 10,000 cm².
Watch out for
- Confusing perimeter with area → Perimeter is a length (single unit like cm); area is in square units (cm²). If asked for fencing, use perimeter; for painting a floor, use area.
- Mixing radius and diameter → Many problems give diameter. Always halve it to get radius before using formulas. Forgetting this makes your answer too large (e.g., a circle's area comes out 4 times too big).
- Ignoring unit conversions → If length is in metres and breadth in centimetres, convert to the same unit first. Mixing units gives absurd answers.
Quick reference
- Square: P = 4a, A = a²; Cube: V = a³, TSA = 6a²
- Rectangle: P = 2(l+b), A = lb; Cuboid: V = lbh, TSA = 2(lb+bh+hl)
- Circle: C = 2πr, A = πr²; Cylinder: V = πr²h, TSA = 2πr(r+h)
- Triangle: A = ½ × base × height; use Heron's formula when only sides are given
- Cone: V = ⅓πr²h, slant height l = √(r²+h²)
Check yourself: 3 questions
1. A rectangular garden has a length of 15 metres and breadth of 8 metres. What is the perimeter of the garden?
2. A square park has a side of 12 metres. If the cost of fencing is Rs. 25 per metre, what is the total cost of fencing the park?
3. A rectangular water tank has length 4 metres, breadth 3 metres and height 2 metres. What is the volume of water it can hold in cubic metres?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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