Question

Find the area of the regular polygon,2√3 and 5

Answer 1

Answer

Correct option is

D

5 cm

△ABC is an equilateral △

∴Area=  

4

3

​  

 

​  

a  

2

=75  

3

​  

⟹ a  

2

=300

a=10  

3

​  

cm

AM=MC=  

2

10  

3

​  

 

​  

=5  

3

​  

cm

Area =  

2

1

​  

×AC×BM

75  

3

​  

=  

2

1

​  

×10  

3

​  

×BM  

∴BM=15cm

△AOC,△BOC and △AOB are of equal area

∴ar(△AOC)=  

3

1

​  

ar(△ABC)=  

3

1

​  

×75  

3

​  

=25  

3

​  

cm  

2

 

In △AOC,

ar(△AOC)=  

2

1

​  

×AC×OM

⇒25  

3

​  

=  

2

1

​  

×10  

3

​  

×OM  

∴OM=5cm Ans.