Page 180 - Math_Genius_V1.0_C6_Flipbook

E:\Working\Focus_Learning\Math_Genius-6\Open_Files\09_Chapter_6\Chapter_6
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Perimeter of a Square

Let us take a square ABCD of side 3 m as shown here. Let us find the perimeter of the square.

3 m
A B

D C
Perimeter of square ABCD = Sum of length of its all sides

= 3 m + 3 m + 3 m + 3 m = 12 m = 4 × 3 m = 4 × length of its side
Thus, we conclude that the perimeter of a square = 4 × side

Perimeter of a Triangle

Let us consider a triangle PQR, having three sides of lengths 3 cm, 5 cm P
and 7 cm. 3 cm 5 cm
Perimeter of DPQR = 3 cm + 5 cm + 7 cm Q R
7 cm
= 15 cm = sum of the lengths of its three sides.
Perimeter of an Equilateral Triangle

Consider an equilateral triangle ABC of 3 cm. Let us find the perimeter of equilateral triangle ABC.
Since perimeter of a triangle = sum of length of its sides A

∴ Perimeter of DABC = 3 cm + 3 cm + 3 cm = 9 cm
= 3 × 3 cm

= 3 × length of a side
B 3 cm C
Thus, we can say, the perimeter of an equilateral triangle = 3 × side

Note: 1. The perimeter of any closed figure is the sum of the lengths of its sides made up of line segments.
2. The units of perimeter are the same as that of length i.e., m, cm, mm, etc.
Perimeter of Regular Polygon

We have just seen that the regular polygon with 3 sides, i.e., an equilateral triangle has perimeter
3 × length of a side, and a regular polygon with 4 sides, i.e., a square has perimeter 4 × length of
a side.

Similarly, the formulae for other regular polygons are as follows:

Regular polygon Number of sides Perimeter
Pentagon 5 5 × length of a side
Hexagon 6 6 × length of a side
Heptagon 7 7 × length of a side
Octagon 8 8 × length of a side

178
Mathematics-6
Mathematics-6 178