How to Solve: Area and Perimeter (2D Figures)

How to Solve: Area and Perimeter (2D Figures)

For SSC / Bank / Railway Exams

Introduction

"Mastering area and perimeter can get you 5–8 marks in SSC, Bank, or Railway exams—enough to push you from ‘just passing’ to ‘top rank.’ Whether it’s a rectangle, triangle, or circle, one wrong formula or unit mistake can cost you the entire question. Today, you’ll learn the exact steps to solve any 2D figure problem—fast and error-free."

What You Need To Know First

Before diving in, ensure you understand: 1. Basic geometry terms (side, length, width, radius, diameter). 2. Units of measurement (cm, m, km, mm) and how to convert them (e.g., 1 m = 100 cm). 3. Basic arithmetic (addition, multiplication, squaring numbers).

Key Vocabulary

Formulas To Know

MEMORIZE THESE—most exams do NOT provide them!

Step-by-Step Method

Follow these 5 steps for EVERY problem:

1. Identify the shape → Look at the figure or description. Is it a rectangle? Circle? Triangle?
2. List the given values → Write down all measurements (e.g., length = 5 cm, width = 3 cm).
3. Choose the correct formula → Pick from the table above based on the shape.
4. Plug in the values → Substitute the numbers into the formula.
5. Calculate and check units → Solve, then add the correct unit (cm² for area, cm for perimeter).

Worked Example Using the Steps

Problem: Find the area and perimeter of a rectangle with length 8 cm and width 5 cm.

1. Identify the shape → Rectangle.
2. List the given values → length (l) = 8 cm, width (w) = 5 cm.
3. Choose the correct formula →
4. Perimeter: P = 2 × (l + w)
5. Area: A = l × w
6. Plug in the values →
7. P = 2 × (8 + 5) = 2 × 13 = 26 cm
8. A = 8 × 5 = 40 cm²
9. Calculate and check units → Perimeter = 26 cm, Area = 40 cm².

Worked Examples

Example 1 – Basic (Rectangle)

Problem: A rectangular field is 12 m long and 7 m wide. Find its perimeter and area.

Solution: 1. Shape → Rectangle. 2. Given → l = 12 m, w = 7 m. 3. Formulas →
- P = 2 × (l + w)
- A = l × w 4. Plug in →
- P = 2 × (12 + 7) = 2 × 19 = 38 m
- A = 12 × 7 = 84 m² 5. Answer → Perimeter = 38 m, Area = 84 m².

What we did and why: - We used the rectangle formulas because the problem described a rectangle. - Units are in meters (m) for perimeter and square meters (m²) for area.

Example 2 – Medium (Triangle with Missing Side)

Problem: A triangle has sides 5 cm, 12 cm, and 13 cm. Its height to the 12 cm base is 5 cm. Find its perimeter and area.

Solution: 1. Shape → Triangle. 2. Given → sides = 5 cm, 12 cm, 13 cm; base (b) = 12 cm, height (h) = 5 cm. 3. Formulas →
- P = sum of all sides
- A = ½ × b × h 4. Plug in →
- P = 5 + 12 + 13 = 30 cm
- A = ½ × 12 × 5 = 30 cm² 5. Answer → Perimeter = 30 cm, Area = 30 cm².

What we did and why: - The perimeter is the sum of all sides. - The area uses the base and height (not the other sides).

Example 3 – Exam-Style (Circle with Diameter)

Problem: The diameter of a circular garden is 14 m. Find its circumference and area. (Use π = 22/7)

Solution: 1. Shape → Circle. 2. Given → diameter (d) = 14 m → radius (r) = d/2 = 7 m. 3. Formulas →
- Circumference (C) = πd or 2πr
- Area (A) = πr² 4. Plug in →
- C = 22/7 × 14 = 44 m
- A = 22/7 × 7 × 7 = 154 m² 5. Answer → Circumference = 44 m, Area = 154 m².

What we did and why: - We converted diameter to radius first (r = d/2). - Used π = 22/7 as given in the problem.

Common Mistakes

Exam Traps

1-Minute Recap

"Night before the exam? Here’s the crash course: 1. Perimeter = add all sides (for rectangles: 2 × (l + w)). 2. Area = space inside (rectangle: l × w, triangle: ½ × b × h, circle: πr²). 3. Circle tricks → radius = half diameter. Circumference = πd or 2πr. 4. Units matter → cm for perimeter, cm² for area. 5. Double-check → Did you use the right formula? Did you convert units? Now go solve 3 problems—you’ve got this!