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Basic Shapes & Formulas (2D Geometry)

Introduction

Geometry begins with understanding simple two-dimensional shapes. In aptitude exams, questions on area and perimeter of basic figures are common and help test your formula application skills.

This pattern helps you quickly solve problems involving Square, Rectangle, Triangle, and Circle using standard formulas.

Pattern: Basic Shapes & Formulas (2D Geometry)

Pattern

The key idea is: Identify the shape → Apply the correct formula for Area or Perimeter → Substitute and solve.

Common Formulas:
• Square → Area = a², Perimeter = 4a
• Rectangle → Area = l × b, Perimeter = 2(l + b)
• Triangle → Area = ½ × base × height
• Circle → Area = πr², Circumference = 2πr

Step-by-Step Example

Question

A rectangular field has a length of 30 m and a breadth of 20 m. Find its area and perimeter.

Solution

  1. Step 1: Identify the shape and data.

    The given shape is a rectangle.
    Length (l) = 30 m, Breadth (b) = 20 m.

  2. Step 2: Apply the formulas.

    Area = l × b
    Perimeter = 2(l + b)

  3. Step 3: Substitute the values.

    Area = 30 × 20 = 600 m²
    Perimeter = 2(30 + 20) = 2 × 50 = 100 m

  4. Final Answer:

    Area = 600 m²
    Perimeter = 100 m

  5. Quick Check:

    Both values are positive and units are consistent (m² for area, m for perimeter) ✅

Quick Variations

1. Finding side when area or perimeter is given.

2. Comparing two shapes with equal area or perimeter.

3. Converting units (cm² to m², etc.) before applying the formula.

Trick to Always Use

  • Step 1: Identify the shape first - never mix formulas.
  • Step 2: Remember: Perimeter → Linear; Area → Squared units.
  • Step 3: Always include correct units (m, m², cm², etc.).

Summary

Summary

In the Basic Shapes & Formulas pattern:

  • Identify the correct geometric shape.
  • Apply the respective formula for area or perimeter.
  • Substitute the given values carefully with correct units.
  • Verify the result with a quick unit check.

Practice

(1/5)
1. Find the area of a square whose side is 12 m.
easy
A. 144 m²
B. 120 m²
C. 150 m²
D. 160 m²

Solution

  1. Step 1: Identify shape and given data.

    Shape = Square; Side = 12 m.

  2. Step 2: Apply formula.

    Area of square = a².

  3. Step 3: Substitute values.

    Area = 12 × 12 = 144 m².

  4. Final Answer:

    Area = 144 m² → Option A.

  5. Quick Check:

    12² = 144 ✅
Hint: For a square, just square the side length.
Common Mistakes: Multiplying by 4 instead of squaring the side.
2. A rectangular plot has a length of 25 m and breadth of 15 m. Find its perimeter.
easy
A. 70 m
B. 80 m
C. 60 m
D. 50 m

Solution

  1. Step 1: Identify shape and data.

    Shape = Rectangle; Length = 25 m, Breadth = 15 m.

  2. Step 2: Apply formula.

    Perimeter = 2(l + b).

  3. Step 3: Substitute values.

    Perimeter = 2(25 + 15) = 2 × 40 = 80 m.

  4. Final Answer:

    Perimeter = 80 m → Option B.

  5. Quick Check:

    Perimeter = 2(40) = 80 ✅
Hint: Add length and breadth first, then multiply by 2.
Common Mistakes: Forgetting to multiply by 2 after adding sides.
3. The base of a triangle is 18 cm and its height is 10 cm. Find its area.
easy
A. 80 cm²
B. 100 cm²
C. 90 cm²
D. 120 cm²

Solution

  1. Step 1: Identify shape and given data.

    Shape = Triangle; Base = 18 cm, Height = 10 cm.

  2. Step 2: Apply formula.

    Area = ½ × base × height.

  3. Step 3: Substitute values.

    Area = ½ × 18 × 10 = 9 × 10 = 90 cm².

  4. Final Answer:

    Area = 90 cm² → Option C.

  5. Quick Check:

    Half of (18×10)=90 ✅
Hint: For triangles, take half the product of base and height.
Common Mistakes: Forgetting to divide by 2 after multiplying base and height.
4. Find the circumference of a circle with radius 7 cm. (Use π = 22/7)
medium
A. 49 cm
B. 50 cm
C. 42 cm
D. 44 cm

Solution

  1. Step 1: Identify given data.

    Radius = 7 cm.

  2. Step 2: Apply formula.

    Circumference = 2πr.

  3. Step 3: Substitute values.

    = 2 × (22/7) × 7 = 2 × 22 = 44 cm.

  4. Final Answer:

    Circumference = 44 cm → Option D.

  5. Quick Check:

    7 cancels with 7, 2×22=44 ✅
Hint: Remember: Circumference = 2 × π × r.
Common Mistakes: Using πr² (area formula) instead of 2πr.
5. A square and a rectangle have the same perimeter of 40 m. The rectangle’s length is 12 m. Find its breadth.
medium
A. 8 m
B. 10 m
C. 12 m
D. 14 m

Solution

  1. Step 1: Identify shape and formula.

    Rectangle’s Perimeter = 2(l + b) = 40.

  2. Step 2: Substitute known values.

    2(12 + b) = 40 → 12 + b = 20 → b = 8.

  3. Step 3: Compute result.

    So breadth = 8 m.

  4. Final Answer:

    Breadth = 8 m → Option A.

  5. Quick Check:

    2(12 + 8) = 40 ✅
Hint: Always halve the perimeter before subtracting the known side sum.
Common Mistakes: Forgetting to divide perimeter by 2 before solving for breadth.

Mock Test

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