Mensuration

About 6 min · Numerical & Mental Ability · English

Time worked out from the lesson's 415 words at 150 words a minute, plus a minute for each question.

Mensuration is the branch of mathematics dealing with measurement of geometric figures — their lengths, areas, surface areas and volumes.

Key ideas

2-D vs 3-D figures: Two-dimensional shapes (plane figures) have area and perimeter; three-dimensional solids have surface area and volume. Don't confuse them in exam pressure.
Perimeter is boundary length: The distance around a closed figure. Used in fencing, framing and border problems. Measured in linear units (m, cm, km).
Area is surface coverage: The space enclosed within a 2-D boundary. Used in flooring, painting flat surfaces and land measurement. Measured in square units (m², cm², hectare).
Surface area for solids: Total area of all outer surfaces of a 3-D object. Lateral (curved) surface area excludes top/bottom. Total surface area includes all faces. Used in painting, wrapping and material estimation.
Volume is space occupied: The three-dimensional capacity of a solid. Used in filling, emptying, capacity and displacement problems. Measured in cubic units (m³, cm³, litre where 1 litre = 1000 cm³).

Watch out for

Using perimeter formula for area: Students often confuse 2(l+b) with l×b. Remember: perimeter is boundary, area is surface. Fix: Read question carefully — "fencing" means perimeter, "flooring/painting" means area.
Forgetting to convert units: Mixing metres and centimetres in the same calculation produces wrong results. Fix: Convert all measurements to the same unit before applying any formula.
Confusing curved and total surface area: For cylinders/cones, curved surface excludes circular bases; total surface includes them. Fix: "Curved/lateral" = sides only; "Total" = all surfaces including top/bottom.

Quick reference

Rectangle: Area = l×b; Perimeter = 2(l+b)
Square: Area = a²; Perimeter = 4a
Circle: Area = πr²; Circumference = 2πr
Triangle: Area = ½ × base × height
Cube: Volume = a³; Surface Area = 6a²

Check yourself: 3 questions

1. A rectangular plot measures 45 m in length and 30 m in breadth. What is the cost of fencing the plot at the rate of Rs. 25 per metre?
2. A cylindrical water tank has a diameter of 14 m and height of 10 m. What is the volume of water it can hold? (Use π = 22/7)
3. The area of a square field is 3600 square metres. A cow is tethered at one corner of the field with a rope of length equal to half the side of the square. What is the area that the cow can graze? (Use π = 22/7)

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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