Question

Difference between the areas of an equilateral triangle of side 6 cm and its circumcircle is​

Answer 1

SOLUTION:-

Side of equilateral triangle = 6 cm

Area of equilateral triangle =

$\frac{ \sqrt{3} }{4} {a}^{2}$

where, a = side lenght of equilateral triangle

So, area of equ. triangle =

$\frac{ \sqrt{3} }{4} {6}^{2} \\ = 9 \sqrt{3} \\ = 15.57 \: cm {}^{2} \: \: (i)$

And to find the area of circumcircle, first we have to find 'R' radius of circumcircle by using formula R =

$\frac{abc}{4 \times \: area \: of \: \: triangle} \\ where \: a \: \: b \: c \: are \: side \: lenght$

So, R = (6×6×6)/(4×9√3)

= (6×36)/(36√3)

= (6/√3)

= 2√3 cm

Area of circumcircle ,

=> πr²

=> πR²

=> (22/7)(2√3)²

=> 37.70 cm² (ii)

By subtracting (i) from (ii) we get ,

=> (37.70) - ( 15.57)

=> 22.13 cm² is the right answer.

Note:-

circumcircle mean a circle that passes through all the vertices of the polygon.

Triangle is also a polygon.

THANKS.