Mensuration
Overview
Mensuration is the branch of mathematics that deals with measuring shapes — finding their perimeter and area. Perimeter is the total length of the boundary of a shape, while area is the amount of surface enclosed inside it. In Class 6, we learn to calculate perimeters and areas of simple shapes like rectangles, squares, and triangles. These concepts are very useful in real life, such as fencing a garden or tiling a floor.
Typed Notes
What is Perimeter?
Perimeter is the total distance around the boundary of a closed figure. To find the perimeter, we add the lengths of all the sides. For a rectangle with length l and breadth b, perimeter = 2 × (l + b). For a square with side s, perimeter = 4 × s. For a triangle with sides a, b, and c, perimeter = a + b + c. Perimeter is measured in units like cm, m, or km. It is used in real life when we need to fence a field or put a border around a picture.
What is Area?
Area is the amount of flat surface enclosed inside a shape. We measure area in square units like cm², m², or km². To find the area of a rectangle, we multiply its length by its breadth: Area = l × b. For a square, Area = side × side = s². We can also find the area of irregular shapes by counting the number of unit squares that fit inside them on a grid. If a square is half-covered, we count two halves as one full square. Area helps us know how much paint, carpet, or tiles we need for a surface.
Perimeter of Regular and Irregular Shapes
A regular shape has all sides equal, like a square or an equilateral triangle. The perimeter of a regular polygon with n sides of length s is n × s. An irregular shape has sides of different lengths, so we add each side separately to get the perimeter. For example, a triangle with sides 3 cm, 4 cm, and 5 cm has perimeter = 3 + 4 + 5 = 12 cm. Always check that all sides are in the same unit before adding. Converting units correctly is very important in mensuration problems.
Using Grids to Find Area
A grid or squared paper helps us estimate the area of any shape, including irregular ones. Each small square on the grid represents one square unit. We count all fully covered squares and add them up. For partly covered squares, if the covered portion is more than half, we count it as 1; if less than half, we count it as 0; if exactly half, we count it as ½. This method works for any shape. For rectangles and squares, the formula gives an exact answer, but the grid method is great for shapes with curved or uneven boundaries.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01Perimeter of a rectangle = 2 × (length + breadth)
- 02Perimeter of a square = 4 × side
- 03Area of a rectangle = length × breadth
- 04Area of a square = side × side
- 051 metre = 100 cm; 1 m² = 10,000 cm²
Important Formulas
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
Find the perimeter of a rectangle whose length is 8 cm and breadth is 5 cm.
Find the area of a square whose side is 7 cm.
A triangle has sides 6 cm, 8 cm, and 10 cm. Find its perimeter.
A rectangular garden is 12 m long and 9 m wide. Find the cost of fencing it at ₹5 per metre.
Find the area of a rectangle whose length is 10 cm and breadth is 6 cm.
Mensuration deals with measuring perimeter and area of shapes. Perimeter is the total boundary length found by adding all sides. Area is the surface enclosed inside a shape. Key formulas: Rectangle — perimeter = 2(l+b), area = l×b; Square — perimeter = 4s, area = s². Areas of irregular shapes can be estimated using a grid by counting unit squares. These skills are essential for solving real-life problems involving land, fencing, and flooring.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.What is the perimeter of a square with side 9 cm?
Q2.Which formula gives the area of a rectangle?
Q3.A rectangle has length 5 cm and breadth 3 cm. What is its area?
Q4.What unit is used to measure area?
Mark karo — dashboard par progress dikhega.