Question

in the figure, ABC is a triangle right angled at A.semicircles are drawn on AB,AC and BC as diameters find the area of shaded region

Answer 1

BC²=AC²+AB²
      =8²+6²
      =64+36
       =100

BC=10cm

Area of biggest semicircle = 1/2 * 3.14 * r²
                                 =0.5*3.14*5*5
                                  =0.5*78.5
                                  =39.25 cm²

Area of 2nd Largest Semicircle = 0.5*3.14*r²
                                                     =0.5*3.14*3²
                                                   =0.5*3.14*9
                                                    =14.13 cm²

Area of smallest Semicircle = 0.5*3.14*r²
                                             =0.5*3.14*4²
                                             =0.5*3.14*16
                                             =25.12 cm²

Area of Triangle = 1/2 *b*h
                         = 0.5*6*8
                            =24 cm²

Area of shaded region = (24+25.12+14.13) - 39.25
                                    = 63.25-39.25
                                    =24 cm²

MARK BRAINLIEST!!

Answer 2

Answer:

24$cm^{2}$

Step-by-step explanation:

Area of the shaded region

= Ar(2 semicircles) - Ar(2 segments)

= Ar (2 semicircles) - [Ar(biggest semicircle - Ar(triangle)]

= $\frac{\pi (r1)^{2} }{2} + \frac{\pi (r2)^{2} }{2} - \frac{\pi R^{2} }{2} + \frac{1}{2}bh$

on substituting the numbers and simplifying the equation we get

= $\frac{11*9}{7} +\frac{11*16}{7} -\frac{11*25}{7} + 24$

= $\frac{11(9+16-25)}{7} + 24\\= \frac{0}{7} + 24\\= 24cm^{2}$