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Class 6 Mathematics: Geometry Basics

Points, lines, line segments, rays, curves, polygons, angles, triangles, circles, perimeter, and area formulas.

Class 6 Mathematics 5 Generated Practice Exercises NCERT Exercise Solutions

⚡ Key Formulas & Core Relations for Geometry Basics

Perimeter of Rectangle = 2(l + b)
Area of Rectangle = l × b
Perimeter of Square = 4 × side, Area = side²
Circumference of Circle C = 2πr = πd (where π ≈ 22/7)

NCERT Textbook Exercise Solutions

1 Solutions
Exercise 10.1 - Q1

Textbook Exercise Problem

Find the perimeter of a rectangle whose length is 40 cm and breadth is 15 cm.

Step-by-Step Verified Solution:

  1. Step 1: Identify given parameters: length l = 40 cm, breadth b = 15 cm.
  2. Step 2: Formula for perimeter of rectangle = 2(l + b).
  3. Step 3: Substitute: P = 2(40 + 15) = 2(55) = 110 cm.
Final Answer: Perimeter = 110 cm
Key Concept / Exam Strategy: Perimeter measures total distance traveled along the outer boundary.

5 AI-Generated Chapter Exercises (Foundation to HOTS)

5 Problems with Full Steps
Generated Exercise #1 Foundation
Question: How many lines can pass through: (a) one given point? (b) two given points?
Core Concept Tested: Fundamental Euclid geometrical axioms
Mentor Hint: Infinite lines through 1 point; exactly one unique line through 2 points.

Step-by-Step Solution:

  1. Step 1: Through a single point, infinitely many lines can be drawn in all directions.
  2. Step 2: Through two distinct points, exactly one and only one straight line can pass.
Verified Answer: (a) Infinitely many lines, (b) Exactly one unique line
Generated Exercise #2 Intermediate
Question: A table-top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table-top?
Core Concept Tested: Perimeter of rectangle with decimal unit conversion
Mentor Hint: Convert mixed units to meters: 2.25 m and 1.50 m.

Step-by-Step Solution:

  1. Step 1: Length l = 2.25 m, Breadth b = 1.50 m.
  2. Step 2: P = 2(l + b) = 2(2.25 + 1.50) = 2(3.75).
  3. Step 3: P = 7.50 m.
Verified Answer: 7.5 meters (or 750 cm)
Generated Exercise #3 Intermediate
Question: Find the side of a square whose perimeter is 64 cm. Also calculate its area.
Core Concept Tested: Square perimeter reversal and area calculation
Mentor Hint: Side = Perimeter / 4; Area = Side × Side.

Step-by-Step Solution:

  1. Step 1: Side s = Perimeter / 4 = 64 / 4 = 16 cm.
  2. Step 2: Area = s² = 16 × 16 = 256 cm².
Verified Answer: Side = 16 cm, Area = 256 cm²
Generated Exercise #4 JEE-NEET Foundation
Question: A room is 4 m long and 3 m 50 cm wide. How many square meters of carpet is needed to cover the floor of the room?
Core Concept Tested: Area of rectangle in practical cost and flooring applications
Mentor Hint: Carpet required = Area of the floor = length × breadth.

Step-by-Step Solution:

  1. Step 1: Length = 4 m, Breadth = 3.5 m.
  2. Step 2: Area = 4 × 3.5 = 14 m².
Verified Answer: 14 square meters
Generated Exercise #5 Advanced HOTS
Question: A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with 4 rows of wires. What is the length of the wire needed in meters?
Core Concept Tested: Multi-layer perimeter calculation with kilometer to meter conversion
Mentor Hint: Calculate single perimeter in meters first, then multiply by 4 rows.

Step-by-Step Solution:

  1. Step 1: Convert dimensions to meters: 0.7 km = 700 m; 0.5 km = 500 m.
  2. Step 2: Single perimeter = 2(700 + 500) = 2(1200) = 2,400 m.
  3. Step 3: For 4 rows of wire: Total wire = 2,400 × 4 = 9,600 m (or 9.6 km).
Verified Answer: 9,600 meters of wire