Question

In the given figure, find the area of shaded region. The diameter of largest semi-circular arc is 14 cm. Three semi-circles are drawn with diameter AK, KM and MB as shown and diameter of that of the two equal smallest semi-circular arcs are 3.5 cm.​

Answer 1

Answer:

Step-by-step explanation:

AK= 3.5cm

MB=3.5cm

AK+MB=7cm

There fore KM=14-7=7

Area of shader region =

(Area of 2 smaller semi- area of 1 Larger semi ) -area of semi circle

( 2pie r^2/2 -pie r^2/2 ) - pie r^2

=(22/7*3.5/2*3.5/2 - (22/7*7/2*7/2)/2 ) - 22/7*7*7

=(19.25/2)-(77/4)-154

163.625

Answer 2

Area of shaded region is 48.09 square centimetre.

Step-by-step explanation:

Given:-Diameter of of largest semicircular arc = 14 cm

$\therefore$ Radius of largest semicircular arc AO = $\frac{14}{2} =7\ cm$

diameter of 2 equal smallest semi-circular arcs, AK=MB = 3.5 cm.

$\therefore$ radius of 2 equal smallest semi-circular arcs (r)=$\frac{3.5}{2} =1.75\ cm$

To find:- Area of shaded region=?

Solution:-

Now,

AB=14 cm,

AB=AK+KM+MB

14=3.5+KM+3.5

$\therefore$ KM=14-7 = 7 cm

Now, Area of 2 smallest semicircle with r=1.75 cm

Area of 2 smallest semicircle $=\frac{2\pi r^{2} }{2}$

Area of 2 smallest semicircle $=\frac{2\times 3.14\times 1.75^{2} }{2} = \frac{2\times 3.14\times 3.06}{2}$

Area of 2 smallest semicircle $=3.14\times 3.06$

Area of 2 smallest semicircle = 9.61 sq.cm -----------(equation 1)

Now, Area of semicircle with KM=7 cm as diameter,

Therefore radius of semicircle = 3.5 cm

Area of semicircle with KM as diameter $=\frac{\pi R^{2} }{2}$

Area of semicircle with KM as diameter= $\frac{ 3.14\times 3.5^{2} }{2}$

Area of semicircle with KM as diameter = $=\frac{3.14\times 12.25}{2}$

Area of semicircle with KM as diameter = 19.23 sq.cm.  --------(equation 2)

Now, Area of largest semicircle with AO=7 cm as radius,

Area of semicircle with AO as radius$=\frac{\pi R^{2} }{2}$

Area of semicircle with AO as radius $=\frac{3.14\times 7^{2} }{2}$

Area of semicircle with AO as radius $=\frac{3.14\times 49}{2}$

Area of semicircle with AO as radius $=\frac{153.86}{2}$

Area of semicircle with AO as radius = 76.93 sq.cm.  ------(equation 3)

Now, Area of shaded region,

Area of shaded region = Area of semicircle with AO as radius - Area of 2 smallest semicircle - Area of semicircle with KM as diameter

Area of shaded region = 76.93-9.61-19.23    -------(from equation 1,2,3)

Area of shaded region = 76.93-28.84

Area of shaded region = 48.09 sq.cm

Therefore area of shaded region is 48.09 square centimetre.