Question

Two semicircles of equal radii are cut out of a semicircle piece of cardboard.Find the area of the shaded portion.(Ans=38.5m^square)​

Answer 1

$\large\bf\underline{Given:-}$

• Two semicircles of equal radii are cut out of a semicircle piece of cardboard.
• Diameter of Bigger semicircle = 14m

$\large\bf\underline {To \: find:-}$

• Area of shaded portion.

$\huge\bf\underline{Solution:-}$

Diameter of Bigger semicircle = 14m

then ,

• Radius of bigger semicircle = 14/2 = 7m

Now radius of bigger semicircle is the diameter of smaller semicircles.

• Now, Radius of smaller semicircles = 7/2 m

$\bf \dag \: area \: of \: semicircle = \frac{ \pi \: {r}^{2} }{2}$

Now,

$\rm \text{Area of bigger semicircle = } \frac{ \frac{22} {7} \times {7}^{2} }{2} \\ \\ \rm \text{Area of bigger semicircle = } \frac{ \frac{22}{ \cancel7} \times \cancel{49}}{2} \\ \\ \rm \text{Area of bigger semicircle = } \frac{22 \times 7}{2} \\ \\ \rm \text{Area of bigger semicircle = } \frac{154}{2} \\ \\ \rm \text{Area of bigger semicircle = }77 {m}^{2}$

Now ,finding area of smaller semicircles :-

$\rm \text{Area of smaller semicircles = } 2( \frac{ \frac{22}{7} \times (\frac{7}{2} ) {}^{2} }{2}) \\ \\ \rm \text{Area of smaller semicircles = } 2(\frac{ \frac{22}{ \cancel7} \times \frac{ \cancel{49}}{4} }{2} ) \\ \\ \rm \text{Area of smaller semicircles = } 2( \frac{ \frac{11 \times 7}{2} }{2} )\\ \\ \rm \text{Area of smaller semicircles = } 2 (\frac{77}{4} ) \\ \\ \rm \text{Area of smaller semicircles = } \frac{154}{4} \: {m}^{2}$

Area of shaded region = Area of bigger semicircle - area of both semicircles.

Area of shaded region = 77 - 154/4

Area of shaded region = (308 - 154)/4

Area of shaded region = 154/4

Area of shaded region = 77/2

• ≫ Area of shaded region = 38.5m²

Answer 2

Step-by-step explanation:

this is th e half answer thankyou