Question

the ratio between the areas of equilateral triangle and circumcircle
​

Answer 1

Answer:

Area of IncircleArea of Circumcircle=πr2πR2=3a2×a212=4.

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Answer 2

Answer:

∴Area of IncircleArea of Circumcircle=πr2πR2=3a2×a212=4.

Step-by-step explanation:

For an equilateral triangle, s=

2

a+b+c

=

2

3a

and Δ=

4

3

a

2

r

2

=(

s

Δ

)

2

=

12

1

a

2

R

2

=(

4Δ

abc

)

2

=

3

1

a

2

∴

Area of Incircle

Area of Circumcircle

=

πr

2

πR

2

=

3

a

2

×

a

2

12

=4