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Example 1: Find the perimeter of a regular pentagon with each side measuring 8 cm.
Solution: This regular closed figure has 5 sides, each with a length of 8 cm.
Therefore,
Perimeter of the regular pentagon = 5 × length of a side = 5 × 8 cm = 40 cm
Example 2: A piece of string is 96 cm long. What will be the length of each side,
if the string is used to form: 8 cm

(a) a square (b) an equilateral triangle (c) a regular hexagon
Solution: Length of string = 96 cm
(a) When the string is used to form a square.
perimeter of a square = 4 × length of each side
96 cm = 4 × length of each side
Therefore, length of each side = 96 cm ÷ 4 = 24 cm
Thus, the length of each side of the square is 24 cm.
(b) When the string is used to form an equilateral triangle.
perimeter of equilateral triangle = 3 × length of each side
96 cm = 3 × length of each side
Therefore, length of each side = 96 cm ÷ 3 = 32 cm
Thus, the length of the side of equilateral triangle is 32 cm.
(c) When string is used to form a regular hexagon.
perimeter of a regular hexagon = 6 × length of each side
96 cm = 6 × length of each side
Therefore, length of each side = 96 cm ÷ 6 = 16 cm
Thus, the length of each side is 16 cm.

Think and Answer

Two regular hexagons of perimeter 24 cm each are joined as shown in the figure. What is the
perimeter of the new figure formed?

Example 3: Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 40 cm.
What is the length of its third side?
Solution: Perimeter of a triangle = Sum of length of its three sides
40 cm = 12 cm + 14 cm + length of third side
40 cm = 26 cm + length of third side
∴ Length of the third side = 40 cm – 26 cm = 14 cm

maths fun

Take a rough sheet of paper or a sheet of newspaper. Cut the paper in
different ways to make a few random shapes. Estimate the perimeter of each
shape and then verify by measuring the boundary with a scale.

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179 P erimeter and Ar ea
Perimeter and Area