Mensuration Class 6 Maths Chapter 10 Notes: Formulas & Key Concepts

Key Terms in Mensuration

Perimeter

The total length of the boundary of a closed two-dimensional figure. It is the distance around the shape.

Area

The measure of the surface or region enclosed by a closed figure. It is the space inside the boundary.

Closed Figure

A shape that begins and ends at the same point, without any breaks in its boundary.

Regular Polygon

A polygon in which all sides are of equal length and all interior angles are of equal measure. Examples: equilateral triangle, square.

Square Unit

The standard unit for measuring area. If the side length is measured in cm, the area is measured in square cm (cm²).

Polygon

A closed figure made up of three or more straight line segments.

Understanding the Difference: Perimeter vs. Area

A common point of confusion for students is the difference between perimeter and area. Think of it this way: if you have a rectangular park, the perimeter is the length of the fence you need to put around its boundary. It is a measure of length, and you find it by adding the lengths of all the sides. The unit for perimeter is a length unit, like metres (m) or centimetres (cm).

On the other hand, the area of the park is the amount of grass you need to cover the entire ground inside the fence. It is a measure of surface or space. You find it by multiplying dimensions, for example, length × breadth for a rectangle. Because you are measuring a two-dimensional space, the unit for area is a square unit, like square metres (m²) or square centimetres (cm²). So, perimeter is a 1-dimensional measurement (a line), while area is a 2-dimensional measurement (a surface).

Must-Remember Formulas

• Perimeter of a Rectangle = 2 × (length + breadth)
• Perimeter of a Square = 4 × length of a side
• Perimeter of an Equilateral Triangle = 3 × length of a side
• Perimeter of any Regular Polygon = Number of sides × length of one side
• Perimeter of an Irregular Polygon = Sum of the lengths of all sides
• Area of a Rectangle = length × breadth
• Area of a Square = side × side or (side)²
• Units for Perimeter are length units: cm, m, km.
• Units for Area are square units: sq. cm (cm²), sq. m (m²), sq. km (km²).

How to Find Area Using a Squared Paper

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Worked Examples

• {"title":"Perimeter of a Rectangle","bodyMarkdown":"Question: Find the perimeter of a rectangular photo frame whose length is 25 cm and breadth is 15 cm.\nSolution:\nFormula: Perimeter = 2 × (length + breadth)\n= 2 × (25 cm + 15 cm)\n= 2 × (40 cm)\n= 80 cm\nAnswer: The perimeter is 80 cm."}
• {"title":"Area of a Square","bodyMarkdown":"Question: A square carrom board has a side of 70 cm. What is its area?\nSolution:\nFormula: Area = side × side\n= 70 cm × 70 cm\n= 4900 sq. cm\nAnswer: The area is 4900 cm²."}
• {"title":"Finding a Missing Side","bodyMarkdown":"Question: The perimeter of a triangle is 22 cm. Two of its sides are 8 cm and 10 cm. Find the length of the third side.\nSolution:\nPerimeter = Side 1 + Side 2 + Side 3\n22 cm = 8 cm + 10 cm + Side 3\n22 cm = 18 cm + Side 3\nSide 3 = 22 cm - 18 cm\nSide 3 = 4 cm\nAnswer: The third side is 4 cm."}

Exam Tip: Avoid Common Mistakes

Pay close attention to units! This is the most common place to lose marks.

• Perimeter is a length, so its unit is cm, m, etc.
• Area is a surface, so its unit is always sq. cm (or cm²), sq. m (or m²), etc.

Never write 'Area = 50 cm'. It should be 'Area = 50 cm²'. In exams, always write the formula first, then substitute the values, and finally write the answer with the correct unit. This shows your method clearly and can get you partial marks even if your final calculation is wrong.

Practice Questions with Solutions

• What is the perimeter of a regular hexagon with each side measuring 5 cm? A regular hexagon has 6 equal sides. Perimeter = 6 × side = 6 × 5 cm = 30 cm.
• If the area of a square is 81 sq. m, what is the length of its side? The side is 9 m, because Area = side × side, and 9 × 9 = 81.
• A rectangle is 10 m long and 8 m wide. What are its perimeter and area? Perimeter = 2 × (10+8) = 36 m. Area = 10 × 8 = 80 sq. m.
• To find the length of lace needed for a saree border, do you need to calculate perimeter or area? Perimeter, because the lace goes around the boundary of the saree.

Frequently Asked Questions

Frequently Asked Questions