Find the Area!

since, radius of of circle = Sides of an equilateral triangle = 5 cm

area of circle = πr^2

                         = 3.14 × 5 ×5 

                          = 3.14  × 25

                          = 78.5

area of equilateral triangle = (√3)/4 a^2

                                              = 1.73 /4 × 5× 5

                                             =0.432× 25

                                           =10.8

area of shaded region = area of circle - area of equilateral triangle

                                        = 78.5 - 10.8

                                       = 67.7

as we know that the area of a triangle is 1/2bh where b is base length and h is height here we have a triangle of each 5cm it is a equilateral triangle so h=perpendicular drawn to the base so h^2=r^2 + r/2^2 where r is radius of the circle or the side length so h^2=25+25/4 (by Pythagoras thm) so h ={(3 25)/4}^1/2 so area =1/2 5*h i.e =10.8 so remaining area = area of circle - area of triangle 78.5-10.8 = 67.7

As area of circle is πr^2 so using this formula area of circle is 78.5 and now using hero formula to calculate the area of equilateral triangle √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2 and hence area of tringle is 10.82 now subtract area of tringle from the area of circle we get the 67. 7.......

Consider my diagram. The area of the shaded region is the area of the circle minus the area of the triangle. We have

$A=\pi(5)^2-\dfrac{\sqrt{3}}{4}(5^2) \approx$ $\boxed{ 67.71}$

Calculate the area of circle and the equilateral triangle and subtract that of triangle from circle