20. Mensuration: 2D figures
Free study material · concepts, shortcuts & solved questions
Rectangle area=lb, perimeter=2(l+b); square area=a², perimeter=4a; triangle area=1/2×base×height; trapezium area=1/2×(sum of parallel sides)×height; circle area=πr². Keep square units for area.
Method before formula For composite figures, split into known shapes and add/subtract. In perimeter questions, count only the outer boundary; internal lines are not part of perimeter unless asked. |
Formula and decision table
Figure | Formula |
Triangle | 1/2 bh |
Trapezium | 1/2(a+b)h |
Sector | Area=(θ/360)πr² |
Regular polygon | 1/2×apothem×perimeter |
Worked understanding
A reliable solution has five visible moves: identify the data, choose the base or unit, write the rule, substitute carefully, and check the size of the answer. The examples in this chapter are deliberately small so that the method remains visible.
Calculation discipline Before pressing ahead, state the denominator or unit in words. For example: profit on CP, discount on MP, average over number of items, speed in metres per second, and probability over the fixed sample space. |
Solved examples from this chapter
Question focus | Correct move | Answer |
Triangle base 10, height 8. Area: | 1/2×10×8=40. | B. 40 |
Rectangle 12×7 perimeter: | 2(12+7)=38. | B. 38 |
Area units are: | Area is measured in square units. | B. Square |
What an examiner is testing
The options around Mensuration: 2D figures usually represent a wrong base, a missed conversion, a sign error or a shortcut used outside its condition. Say the base and unit before calculating, estimate the result, and use substitution or a reverse operation as the final check.
Step-by-step answer construction
Example 1: Triangle base 10, height 8. Area: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 40, because 1/2×10×8=40.
Example 2: Rectangle 12×7 perimeter: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 38, because 2(12+7)=38.
Example 3: Area units are: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is Square, because Area is measured in square units.
Chapter practice
1. Triangle base 10, height 8. Area:
(A) 18 (B) 40 (C) 80 (D) 160
Answer: B. 40 | Explanation: 1/2×10×8=40.
2. Rectangle 12×7 perimeter:
(A) 19 (B) 38 (C) 84 (D) 168
Answer: B. 38 | Explanation: 2(12+7)=38.
3. Area units are:
(A) Linear (B) Square (C) Cubic (D) No unit
Answer: B. Square | Explanation: Area is measured in square units.
SSC CGL speed and trap clinic
For Mensuration: 2D figures, speed comes after classification. Before calculating, say aloud what the number means, what the denominator is, and what unit the answer must carry. Then use the nearest-option check to catch a sign, base or conversion error.
Checkpoint | What to verify | Typical SSC mistake |
Base | Which quantity is the base in Mensuration: 2D figures? | Using selling price instead of cost price, or part instead of total |
Unit | Are time, distance, area and rate in compatible units? | Mixing hours with minutes or km/h with m/s |
Direction | Should the answer increase, decrease or stay bounded? | Accepting an impossible negative length or probability above 1 |
Estimate | What range should the answer lie in before exact work? | Trusting a long calculation that is far from the options |
Reverse check | Can the answer be substituted back into the condition? | Stopping at an algebraic value without verification |
Mini decision drill
1. Write the first operation you would perform in a Mensuration: 2D figures question and why.
2. State the most dangerous denominator or unit in this chapter.
3. Give one condition under which a shortcut would be invalid.
4. Create a small numerical example and verify it by a second method.
Revision evidence Do not tick this chapter because you recognised the formula. Tick it only after you solve one direct question, one altered-condition question and one mixed-paper question correctly. |