Mensuration
About 6 min · Elementary Mathematics · English
Time worked out from the lesson's 416 words at 150 words a minute, plus a minute for each question.
This topic tests your ability to calculate areas, perimeters, surface areas, and volumes of common two-dimensional and three-dimensional shapes. Most problems are formula-based with straightforward numerical substitution, though some require two-step reasoning (for example, finding the radius first before calculating area).
Key ideas
- Area measures the surface enclosed by a 2-D figure, expressed in square units (cm², m², etc.). Perimeter measures the boundary length, expressed in linear units (cm, m, etc.).
- Surface area of a 3-D object is the total area covering all its outer faces. Volume measures the space inside a 3-D object, expressed in cubic units (cm³, m³, litres).
- For composite figures (e.g., a path around a rectangle, or a figure made of a rectangle and semicircle), break the shape into simpler parts and add or subtract areas as needed.
- Diagonal of a rectangle = √(length² + breadth²). Diagonal of a square with side a = *a*√2. These often appear as intermediate steps in multi-step problems.
- The ratio of the circumference of a circle to its diameter is π (pi), approximately 22/7 or 3.14.
Watch out for
- Confusing radius and diameter: The question gives diameter 10 cm, but you use 10 as radius in πr². Always halve the diameter to get radius.
- Mixing up perimeter and area formulas: For a rectangle, writing Area = 2(l + b) instead of Perimeter. Double-check which quantity the question asks for.
- Forgetting unit conversions: Calculating area in metres when dimensions are in centimetres, or vice versa. Convert all measurements to the same unit before applying formulas.
Quick reference
- Rectangle: A = l×b, P = 2(l+b); Square: A = a², P = 4a
- Circle: A = πr², C = 2πr; Semicircle: A = πr²/2, P = πr + 2r
- Triangle: A = ½×base×height; Equilateral: A = (√3/4)a²
- Cube: V = a³, TSA = 6a²; Cuboid: V = l×b×h, TSA = 2(lb+bh+hl)
- Cylinder: V = πr²h, CSA = 2πrh; Cone: V = (1/3)πr²h, CSA = πrl
Check yourself: 3 questions
1. A rectangular park is 45 m long and 30 m wide. What is the cost of fencing it at the rate of Rs 12 per metre?
2. The area of a square field is 2025 square metres. Find the length of its diagonal.
3. A cylindrical water tank has a radius of 1.4 m and a height of 5 m. How many litres of water can it hold? (Use π = 22/7 and 1 cubic metre = 1000 litres)
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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