Question

which of the following shapes has greater area of polygon
full solution
​

Answer 1

Answer:

LetthegivenperimeterbeP.

Wecalculatetheareasofthegivenfigures

andcompare.

OptionA⟶circle.

Theperimeter(circumference)=P

⟹2πr=P(whenr=radiusofthecircle.)

⟹r=  

2π

P

​

 

∴ar.circle=πr  

2

=π×(  

2π

P

​

)  

2

=  

4×3.14

P  

2

 

​

=  

12.56

P  

2

 

​

.

OptionB⟶Equilateraltriangle.

Oneside=  

3

P

​

.

∴area=  

4

3

​

 

​

side  

2

=  

4

3

​

 

​

×(  

3

P

​

)  

2

=  

20.77

P  

2

 

​

.

OptionC⟶Square

side=  

4

P

​

 

∴area=  

4

P

​

×  

4

P

​

=  

16

P  

2

 

​

.

OptionD⟶Regularpentagon.

side=  

5

P

​

.

∴ar.pentagon=  

4

1

​

 

5(5+2  

5

​

)

​

×side  

2

 

=  

4

1

​

 

5(5+2  

5

​

)

​

×(  

5

P

​

)  

2

=  

19.95

P  

2

 

​

.

∴comparingtheareasweget

thear.circleisthegreatest.

Ans−OptionA