Summary
Chapter 6 of Ganita Prakash (Class 6 Maths) covers Perimeter and Area — teaching students to calculate the boundary length (perimeter) and the enclosed region (area) of rectangles, squares, triangles, and regular polygons using formulas and grid-based estimation.
This chapter builds on students' prior knowledge to establish formulas for perimeter and area of common shapes. Perimeter of a rectangle is 2 × (length + breadth), of a square is 4 × side, and of an equilateral triangle is 3 × side. Area of a rectangle equals length × width and area of a square equals side × side. The chapter also introduces triangle areas as half the enclosing rectangle's area, explores area estimation on squared grid paper using four counting conventions, and investigates how the same area can yield different perimeters and vice versa through hands-on puzzles including tangram exploration and house plan problems.
Key points & formulas
- 01Perimeter of a polygon = sum of the lengths of all its sides.
- 02Perimeter of a rectangle = 2 × (length + breadth).
- 03Perimeter of a square = 4 × side length.
- 04Perimeter of an equilateral triangle = 3 × side length.
- 05General formula for any regular polygon: perimeter = number of sides × length of one side.
- 06Area of a rectangle = length × width; area of a square = side × side.
- 07Area of a triangle = half the area of a rectangle with the same base and height.
- 08Area is measured in square units; it is estimated on grid paper using four conventions (full square = 1, less than half = ignore, more than half = 1, exactly half = ½).
- 09Squares are used as units of area because they tessellate perfectly without gaps, unlike circles.
- 10Two figures can have the same area but different perimeters, or the same perimeter but different areas.
Frequently asked questions
01What is this chapter about?
Chapter 6 of Class 6 Maths (Ganita Prakash) is about Perimeter and Area. It teaches how to find the boundary length (perimeter) and the enclosed region (area) of rectangles, squares, triangles, and regular polygons, and explores the relationship between the two measures.
02What is the formula for the perimeter of a rectangle?
The perimeter of a rectangle = 2 × (length + breadth). For example, a rectangle 12 cm long and 8 cm wide has perimeter = 2 × (12 + 8) = 40 cm.
03What is the formula for the perimeter of a square?
The perimeter of a square = 4 × side length. For example, a square of side 1 m has perimeter = 4 × 1 = 4 m.
04What is the formula for the area of a rectangle?
Area of a rectangle = length × width. For example, a floor 5 m long and 4 m wide has area = 5 × 4 = 20 sq m.
05How is the area of a triangle related to a rectangle?
The area of a triangle equals half the area of a rectangle with the same base and height. Cutting any rectangle along its diagonal produces two triangles of equal area, each equal to half the rectangle's area.
06Can two figures have the same area but different perimeters?
Yes. The chapter uses Charan's house (35 ft × 30 ft) and Sharan's house (42 ft × 25 ft) as an example — both have the same area of 1050 sq ft, but Charan's perimeter is 130 ft and Sharan's is 134 ft.
07How do you estimate area using squared (graph) paper?
The chapter gives four conventions: (1) a full square counts as 1 sq unit, (2) portions less than half a square are ignored, (3) portions more than half a square count as 1 sq unit, and (4) exactly half a square counts as ½ sq unit.
08Why is area measured in square units and not in circular units?
Circles cannot be packed tightly without gaps, making area measurement inaccurate. Squares tessellate perfectly with no gaps or overlaps, giving precise measurement. The chapter shows that the same rectangle packed with circles gives different counts depending on the packing pattern (42 or 44 circles).
09What is the perimeter of a regular polygon?
The perimeter of any regular polygon = number of sides × length of one side. For an equilateral triangle (3 sides) it is 3 × side; for a regular hexagon (6 sides) it is 6 × side, etc.
10What happens to perimeter when a new unit square is added to a figure?
Depending on how many sides the new square shares with existing squares, the perimeter can increase, decrease, or stay the same. The chapter explores all three possibilities.
11Among all rectangles with the same area, which has the greatest and which has the least perimeter?
For a fixed area, the most elongated rectangle (like 24 × 1) has the greatest perimeter, and the rectangle closest to a square (like 6 × 4 for area 24) has the least perimeter.
12Is the NCERT Ganita Prakash Class 6 Chapter 6 PDF free to download with no sign-up?
Yes, the NCERT Ganita Prakash Class 6 Chapter 6 PDF is available free to download with no sign-up required on CBSE Prep Master.
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This is the complete Ganita Prakash Chapter 6 as published by NCERT — every diagram, solved example, and exercise included, free. Browse all NCERT Class 6 textbooks.
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