Pariksha SaathiMensuration Questions with Solutions (Area and Perimeter)
Mensuration questions are mostly about picking the right formula and plugging in carefully — the shapes themselves are simple. Here’s the concept, four fully worked examples, and a few to try yourself.
The concept, quickly
- Perimeter is the distance around a shape; area is the space it covers. Rectangle: Perimeter = 2(length + breadth), Area = length × breadth. Square (a rectangle with equal sides): Perimeter = 4 × side, Area = side².
- Circle: Circumference = 2πr, Area = πr². Use π ≈ 22/7 when the radius is a multiple of 7 (it cancels cleanly); otherwise use π ≈ 3.14.
- Triangle: Area = (1/2) × base × height. For a right-angled triangle specifically, the two legs meeting at the right angle can be used directly as base and height.
- For "path around a field" or "border" questions, find the outer shape’s area and the inner shape’s area separately, then subtract — don’t try to compute the path’s area directly as one piece.
Worked examples
1. Find the area and perimeter of a rectangle with length 15 m and breadth 8 m.
Solution
- Area = length × breadth = 15 × 8 = 120 m²
- Perimeter = 2(length + breadth) = 2(15 + 8) = 2 × 23 = 46 m
Answer: Area = 120 m², Perimeter = 46 m
2. A circular park has a radius of 14 m. Find its area. (Use π = 22/7.)
Solution
- Area = πr² = (22/7) × 14 × 14
- 14 is a multiple of 7, so it cancels cleanly: (22/7) × 14 = 44, then 44 × 14 = 616
Answer: 616 m²
3. Find the area of a right-angled triangle with base 12 cm and height 9 cm. Also find the length of its hypotenuse.
Solution
- Area = (1/2) × base × height = (1/2) × 12 × 9 = 54 cm²
- Hypotenuse = √(base² + height²) = √(12² + 9²) = √(144 + 81) = √225 = 15 cm
Answer: Area = 54 cm², Hypotenuse = 15 cm
4. A rectangular garden is 20 m long and 15 m wide. A path 2.5 m wide is built all around it, on the outside. Find the area of the path.
Solution
- The path adds 2.5 m on every side, so the outer rectangle is (20 + 2×2.5) by (15 + 2×2.5) = 25 m by 20 m.
- Outer area = 25 × 20 = 500 m². Garden (inner) area = 20 × 15 = 300 m².
- Area of the path = outer area − inner area = 500 − 300 = 200 m²
Answer: 200 m²
Try these yourself
Work through these the same way, then check against the answer.
1. Find the area and perimeter of a rectangle with length 18 m and breadth 10 m.
Answer: Area = 180 m², Perimeter = 56 m
2. A circular garden has a radius of 21 m. Find its area. (Use π = 22/7.)
Answer: 1,386 m²
3. Find the area of a right-angled triangle with base 10 cm and height 24 cm. Also find its hypotenuse.
Answer: Area = 120 cm², Hypotenuse = 26 cm
Where this comes up
Mensuration is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk.
Practice more Mensuration questions
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