Class 6 Maths Chapter 6: Perimeter and Area Notes

What is perimeter?

The perimeter of a closed figure is the distance covered along its boundary when you go around it once. For a polygon (a closed figure made of line segments), it is the sum of the lengths of all its sides. Perimeter is a length, so we write it in cm, m and so on.

Which perimeter formulas should you know?

• Rectangle: opposite sides are equal, so perimeter = length + breadth + length + breadth = 2 × (length + breadth).
• Square: all four sides are equal, so perimeter = 4 × side.
• Triangle: add the three sides. For an equilateral triangle, perimeter = 3 × side.
• Regular polygon (all sides and all angles equal): perimeter = number of sides × length of one side.

What is area?

Area is the amount of region enclosed by a closed figure. We measure it in square units: a square of side 1 cm has an area of 1 sq cm. Squares are used because they fit together with no gaps and no overlaps.

• Rectangle: area = length × breadth.
• Square: area = side × side.
• Triangle: a diagonal cuts a rectangle into two equal triangles, and any triangle drawn on the rectangle’s base with its top corner on the opposite side covers half of the rectangle.

How do you estimate the area of an odd shape?

Trace it on squared paper. Count every full square as 1 sq unit, count a square that is more than half covered as 1, count exactly half as ½, and leave out squares that are less than half covered.

Can two shapes have the same area but different perimeters?

Yes. Rectangles of area 24 sq units can be 1 × 24 (perimeter 50 units), 2 × 12 (28 units), 3 × 8 (22 units) or 4 × 6 (20 units). The longer and thinner the rectangle, the bigger its perimeter; the closer it is to a square, the smaller its perimeter.