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In figure 2, ABC is a right-angled triangle at A. Semi-circles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.

 

 

 

 
 
 
 
 

Answers (1)

In  \bigtriangleup ABC, by using pythagoras theorem we get

BC^2=AC^2+AB^2

            =8^2+6^2

            =64+36

            = 100

BC = 10 \; cm

\text{Area of biggest semicircle}= \frac{1}{2}\times 3.14\times r^2

                                                 = \frac{1}{2}\times 3.14\times 5\times 5

                                                 = 39.25 \; cm^2

Area of 2^{nd} largest semicircle 

= 0.5 \times 3.14 \times 3^2

= 14.13 \; cm^2

Area of smallest semicircle = 0.5 \times 3.14 \times 4^2

                                            = 25.12 \; cm^2

\text{Area of shaded region} = (24+25.12+14.13)-39.25

                                                 = 63.25 -39.25

                                                  = 24 \; cm^2

 

 

Posted by

Ravindra Pindel

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