Page 197 - Start Up Mathematics_6

Example 3: A rectangular piece of land measures 0.8 km by 0.3 km. Each side is to be fenced
with 3 rows of wires. What is the length of the wire needed?

Solution: Length of the piece of land = 0.8 km
Breadth of the piece of land = 0.3 km

Perimeter of the piece of land = 2(Length + Breadth)
= 2(0.8 + 0.3) km = 2.2 km

Since each side is to be fenced thrice, therefore the length of the wire needed
= 3(2.2 km) = 6.6 km
Example 4: Find the perimeter of each of the following shapes:

(a) A scalene triangle of sides 6 cm, 7 cm and 8 cm
(b) An equilateral triangle of side 5 cm

(c) An isosceles triangle with equal sides 9 cm each and third side 5 cm
Solution: (a) Perimeter of a scalene triangle = Sum of measures of its sides

= 6 + 7 + 8 = 21 cm
(b) Perimeter of an equilateral triangle = 3 × Side = 3 × 5 cm = 15 cm

(c) Perimeter of an isosceles triangle = Sum of measures of its sides
= 9 + 9 + 5 = 23 cm
Example 5: Find the perimeter of a regular pentagon with each side measuring 7 m.

Solution: Perimeter of a regular pentagon = 5 × Side = 5 × 7 m = 35 m
Example 6: The perimeter of a regular hexagon is 84 cm. How long is its side?

Solution: Perimeter of a regular hexagon = 6 × Side

Perimeter of a regular hexagon 84
∴ Each side = = = 14 cm
6 6
Example 7: A piece of string is 36 cm long. What will be the length of each side if the string is
used to form (a) an equilateral triangle, (b) a square, (c) a pentagon, (d) a regular
hexagon.

Solution: Length of string = Perimeter of the figure
(a) Perimeter of an equilateral triangle = 3 × Side = 3 × l
Perimeter 36
∴ Side of an equilateral triangle (l) = = = 12 cm l
3 3
(b) Perimeter of a square = 4 × Side = 4 × l

Perimeter 36
∴ Side of a square (l) = = = 9 cm l
4 4
(c) Since the pentagon is not regular, it is not possible to find the length of its sides.

(d) Perimeter of a regular hexagon = 6 × Side = 6 × l

∴ Side of a regular hexagon (l) = Perimeter = 36 = 6 cm
6
6
l
189