Question

Find the area of the shaded regions:
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Answer 1

Step-by-step explanation:

Usually, we would subtract the area of a smaller inner shape from the area of a larger outer shape in order to find the area of the shaded region.

Answer 2

$\sf\Large{\underline{\underline{Answer:-}}}$

Let us find the diagonal by Pythagoras theorm

Where,

• Base = 12cm
• Perpendicular = 5cm
• Hypotenuse = ?

Formula:-

$\bf{\underline\green{H² \: = \: P² \: + \: B²}}$

Substitute the values,

H² = 5² + 12²

H² = 25 + 144

H² = 169

H = $\sqrt{169}$

H = 13cm

${\bold\blue{Since,\: Diameter}}$ of circle = 13cm

Now, finding radius

$\begin{gathered}\\\;\sf{:\rightarrow\;\; Radius\;=\;\bf{\dfrac{Diameter}{2}\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\; Radius\;=\;\bf{\dfrac{13}{2}\:}}\end{gathered}$

${\bold\blue{Radius}}$ = 6.5cm

✢ Area of circle:

We know that,

Area = $\huge\bf{\underline\green{π\:r²}}$

Substitute the values.

$\begin{gathered}\\\;\sf{:\rightarrow\;\;Area\;of\;circle\;=\;\bf{\dfrac{22}{7}\:\times\:6.5\:\times\:6.5}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;Area\;of\;circle\;=\;\bf{\dfrac{22}{7}\:\:\times\:42.25}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\; Area\;=\;\bf{\dfrac{929.5}{7}\:}}\end{gathered}$

Area = $\sf{\cancel\dfrac{929.5}{7}}$= 132.78 cm

${\bold\blue{Now,}}$

✢Area of rectangle:-

Where,

• Length = 12cm
• Breadth = 5cm

We know that,

Area = $\bf{\underline\green{length \: × \: breadth}}$

$\Longrightarrow$Area = 12 × 5

$\Longrightarrow$Area = 60cm

Now to find the shaded region,

✢Shaded region = Area of Circle – Area of Rectangle

Shaded region = 132.78 – 60

Shaded region = 72.78cm.

${\bold\blue{Hence,}}$

Area of shaded region = 72.78cm