Question

find the area of the shaded region ​

Answer 1

➡️ Area of Shaded region = Area of semicircle - Area of inscribed circle

Now , diameter of inscribed circle is radius of semicircle.

➡️ Diameter of circle = 2×4

➡️ 8 cm

Therefore, radius of semicircle = 8 cm

Now , we will find area of inscribed circle.

Area of circle = π r²

➡️Area of inscribed circle = π× 4²

➡️ 16π cm²

Area of semicircle = (1/2) × π × r²

➡️(1/2) × π × (8)²

➡️32 π cm²

➡️ Area of Shaded region = 32 π - 16π

➡️ Area of Shaded region = 16 π

➡️ Area of Shaded region = 16 × 3.14

➡️ Area of Shaded region = 50.24 cm²

Answer : 50.24 cm²

Answer 2

${\large{\bold{\rm{\underline{Required \; Solution}}}}}$

Question is given in attachment !

Let's solve this question properly,

☑️ This question says that we have to find the area of given shaded region. And according to the figure we have see that the radius of the circle is 4 cm given. And some region of that figure is shaded or some isn't shaded. There are 2 circle's given here as semi · circle and an inscribed circle too.

_____________

~ Firstly let us find the value of radius of semi · circle

According to the figure, the diameter of the inscribed circle is the radius of given semi · circle

As it's given that radius is 4 cm so we have to find the diameter of the given inscribed circle !

Diameter of circle ☞

• ➝ Diameter = 2 × Radius
• ➝ Diameter = 2 × 4
• ➝ Diameter = 8 cm

${\frak{Diameter \: of \: inscribed \: circle \: is \: 8 \: cm}}$

Henceforth,

${\frak{Radius \: of \: semi - \: circle \: is \: 8 \: cm}}$

_____________

~ Now let's find the area of inscribed circle

To find the area of inscribed circle we have to use the formula to find area of circle and it's already known to us. It's πr²

[Now let's just put the values]

Area of circle (inscribed) ☞

• ➝ Area = πr²
• ➝ Area = π4²
• ➝ Area = π16 cm²

_____________

~ Now let's find the area of semi circle

To find the area of semi circle we have to use the formula to find area of semi circle and it's already known to us. It's ½πr²

[Now let's just put the values]

Area of semi circle ☞

• ➝ Area = ½πr²
• ➝ Area = ½π8²
• ➝ Area = ½π64
• ➝ Area = π32 cm²

_____________

~ Now let's find the area of shaded portion

• ➝ Area of shaded portion = Area of semi circle - Area of inscribed circle

• ➝ Area of shaded portion = 32π² - 16π²

• ➝ Area of shaded portion = 16π²

• ➝ Area of shaded portion = 16 × 3.14

Because value of π is 3.14 or 22/7 ( you can take it as you want )

• ➝ Area of shaded portion = 50.24 cm²

_____________

~ Why we not find the area of circle (inscribed) and semi circle fully ? Why we just put values ? We did it because as the question says that we just have to find the area of shaded portion so we haven't to find the area of circle (inscribed) and semi circle fully. And that's the reason that Area of shaded portion = Area of semi circle - Area of inscribed circle implies here !.