untitled

? Area of 'OAB = ah
2

1

= 2 2 tanθ
1 a
au

= ̧ ̧
¹

·

̈ ̈

©

§



n

a $ 180 $

tan 90

4

2

= ̧ ̧
¹

·

̈ ̈

©

§

n

a 180 $

4 cot

2

? Area of a regular polygon having n sides = ̧ ̧
¹

·

̈ ̈

©

§

n

a 180 $

cot

4

2

.

Example 8. If the length of each side of a regular pentagon is 4 cm, determine its
area.
Solution : Let, length of each side of a regular pentagon is a 4 cm.
and number of sides n 5

We know, area of a regular polygon =
n

a 180 $

cot

4

2

? Area of the pentagon =
5

180

cot

4

42 $

Sq. cm.

= 4 ucot 36 o sq. cm.
= 4 u 1 ˜ 376 sq. cm. [with the help of calculator]
= 5 ˜ 506 sq. cm. (approx.)
The required area = 5 ˜ 506 sq. cm. (approx.)
Example 9. The distance of the centre to the vertex of a regular hexagon is 4 m.
Determine its area.
Solution : Let, ABCDEF is a regular hexagon whose centre is O, O is joined to
each of the vertex and thus 6 triangles of equal area are formed.

? $

$

60

6

360

‘COD

Let the distance of centre O to its vertex is a m.
? a = 4.

? Area of 'COD =^22
4

3

2

3

2

1

sin 60

2

1

a˜a $ a˜ a

= 42
4

3

u sq. m. = 43 sq. m.

?Area of the regular hexagon