Area and Perimeter
📋 Quick-reference guides with key formulas and must-know concepts. Perfect for daily practice, last-minute revision, and on-the-go learning.
Cheat Sheets
Study MaterialArea and Perimeter Cheat Sheet
Area and Perimeter is one of the most important and frequently asked topics in Quantitative Aptitude and Mensuration for SSC, Banking, Railway, UPSC, Defence, Insurance, CAT, and other competitive examinations.
This cheat sheet helps candidates understand formulas of 2D figures, area and boundary calculations, paths and shaded region problems, fencing and carpeting concepts, and shortcut techniques for solving mensuration-based questions quickly and accurately in exams.
About This Cheat Sheet
Complete guide to Area and Perimeter for competitive exams:
Basic Concepts
- Perimeter = Boundary Length
- Area = Region Enclosed
- Units of Measurement
- Mensuration Basics
Square & Rectangle
- Square Area & Perimeter
- Rectangle Area & Perimeter
- Diagonal Concepts
- Dimension Change Problems
Triangle Concepts
- Area = ½ × Base × Height
- Heron's Formula
- Perimeter of Triangle
- Special Triangle Problems
Circle & Semi-circle
Circumference, area, sector, arc length, and semi-circle calculations.
Quadrilaterals
- Parallelogram
- Rhombus
- Trapezium
- General Quadrilateral
Paths & Shaded Regions
- Area of Paths
- Cross Path Problems
- Circular Rings
- Shaded Area Problems
Practical Applications
- Cost of Fencing
- Cost of Carpeting
- Area Change Problems
- Dimension Variation
Shortcut Tricks
Fast solving methods, mensuration shortcuts, and exam-oriented geometry techniques.
Topics Covered
| Topic | Description |
|---|---|
| Square | Perimeter = 4a, Area = a² |
| Rectangle | Perimeter = 2(l+b), Area = l×b |
| Triangle | Perimeter and area calculations |
| Heron's Formula | Area using semi-perimeter |
| Circle | Circumference = 2πr, Area = πr² |
| Semi-circle | Area and perimeter calculations |
| Sector of Circle | Arc length and sector area formulas |
| Parallelogram | Area = Base × Height |
| Rhombus | Area = ½ × d₁ × d₂ |
| Trapezium | Area using parallel sides and height |
| Area of Paths | Area around or inside figures |
| Circular Ring | Area between two concentric circles |
| Fencing & Carpeting | Perimeter and area applications |
| Shortcut Tricks | Fast solving methods for exams |
Why This Cheat Sheet is Important
Understand Mensuration Concepts
↓
Improve Formula Application Skills
↓
Apply Shortcut Techniques
↓
Solve Geometry Problems Faster
↓
Score Better in Exams
Competitive Exams Covered
- SSC CGL
- SSC CHSL
- Bank PO & Clerk
- Railway Exams
- UPSC CSAT
- Defence Exams
- Insurance Exams
- State Government Exams
- MBA Entrance Exams
Quick Examples
Example 1:
Find the perimeter of a square having side 12 cm.
Perimeter = 4 × Side
= 4 × 12
= 48 cm
Example 2:
Find the area of a rectangle having length 15 cm and breadth 8 cm.
Area = Length × Breadth
= 15 × 8
= 120 cm²
Example 3:
Find the area of a triangle with base 10 cm and height 6 cm.
Area = ½ × Base × Height
= ½ × 10 × 6
= 30 cm²
Example 4:
Find the circumference of a circle with radius 7 cm.
Circumference = 2πr
= 2 × 22/7 × 7
= 44 cm
Example 5:
A rectangular garden is 20 m long and 15 m broad. Find the cost of fencing at ₹12 per meter.
Perimeter = 2(l+b)
= 2(20+15)
= 70 meters
Cost of fencing =
70 × 12 = ₹840
Final Takeaway
This Area and Perimeter Cheat Sheet provides complete revision material for all major concepts frequently asked in competitive examinations. Regular practice of mensuration formulas, path and shaded region problems, area-perimeter applications, and shortcut techniques can significantly improve speed, accuracy, and geometry problem-solving ability.
It is highly useful for quick revision before exams and helps candidates strengthen the foundation of Quantitative Aptitude.
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