Q. 55.0( 1 Vote )

# In the figure, l(

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 = πr^{2}

Area of semicircle = πr^{2}/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 cm^{2}.

__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 = πr^{2}

⇒ Area = 22/7 × 3.5^{2}

⇒ Area = (22 × 3.5 × 3.5)/7

⇒ Area = 269.5/7 = 38.5 cm^{2}

Thus, total area of the shaded part is 38.5 cm^{2}.

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