Answer :

Given: AB = 14 cm & AM = MB

Clearly, AB = AM + MB


AB = AM + AM = 2 AM


AM = AB/2


AM = 14/2 = 7 cm


Also, area of circle is given by


Area = πr2


Area of semicircle = πr2/2


Now, if diameter of one of the semicircle = 7 cm


Then, radius of that semicircle = 7/2 = 3.5 cm


So, area of that semicircle


…(i)


Radius of the other semicircle = 7/2 = 3.5 cm


So, area of that other semicircle


…(ii)


Adding equations (i) and (ii), we get


Total area of the shaded part = 19.25 + 19.25


= 38.5 cm


Thus, total area of the shaded part is 38.5 cm2.


Alternate Method:


Given that AB = 14 cm & AM = MB


Notice, AB = AM + MB


AB = AM + AM


AB = 2 AM


AM = AB/2


AM = 14/2 = 7 cm


So, if AM is joined with MB, then it forms a complete circle of diameter, 7 cm.


Then, radius of this circle = 7/2 = 3.5 cm


When points A and B are met together, they form a circle.


Let AB = L and center of this circle = O.


Then, we have LM = 7 cm and LO = OM = 3.5 cm (radius).



Area of this circle is given by


Area = πr2


Area = 22/7 × 3.52


Area = (22 × 3.5 × 3.5)/7


Area = 269.5/7 = 38.5 cm2


Thus, total area of the shaded part is 38.5 cm2.


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