Question

please solve this sum by step by step​ and i will mark as brainlist​

Answer 1

ANSWER-

$By\ Pythagoras\ Theoram,\\AC^2=AB^2+BC^2\\So,\ AC=\sqrt{12^2+5^2}\\Therefore,\ AC=\sqrt{169}So,\\AC=13cm\\Now,\\area\ of\ rectangle=\ L×B\\So, ar(ABCD)=12×5=60cm^2\\Now,\\AC=13cm\\So,\ OC=6.5cm\\Now,\\Area\ of\ circle=\ πr^2\\So, area\ of\ circle=3.14×(6.5)^2\\= 132.665cm^2\\Therefore,\ area\ of\ shaded\ region,\\=Area\ of\ circle-Area\\ of\ rectangle\\=132.665cm^2-60cm^2\\=72.665cm^2\\\\\\Hope\ it\ helps....\\Please\ mark\ as\ brainliest.$

Answer 2

Solution

Given :-

• Side of rectangle ABCD (AB) = 12 cm
• Side of BC = 5 cm

Find :-

• Area of shaded region

Explanation

Using Formula

★ Area of circle = πr²

★ Area of rectangle = Length * Width

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Case(1):-

First ,calculate area of rectangle ABCD

==> Area of rectangle = Length * Width

==> Area of rectangle = 12 * 5

==> Area of rectangle = 60 cm²

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Now, Calculate diagonal " AC " of rectangle ABCD

By, Pythagoras's Theorem

★ (Hypotenuse)² = (perpendicular ) ² + (Base)²

So,

==> (Hypotenuse)² = 12² + 5²

==> (Hypotenuse)² = 144 + 25

==> (Hypotenuse)² =169

==> (Hypotenuse)= √169

==> (Hypotenuse) = 13 = AC

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Here, Hypotenuse (AC) of rectangle ABCD be " Diameter " of circle

So, Radius will be = 13/2 = 6.5 cm

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Case(2):-

Now, Calculate Area of circle

==> Area of circle = πr²

==> Area of circle = 3.14 * (6.5)²

==> Area of circle = 3.14 * 42.25

==> Area of circle = 132.665 cm²

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Now, Calculate Area of shaded region

Area of Shaded region be , if we Subtract area of rectangle ABCD from Area of circle

So,

==> Area of Shaded region = Area of circle - Area of rectangle

==> Area of Shaded region = 132. 665 - 60

==> Area of Shaded region = 72.665 cm²

Hence

• Area of Shaded region will be = 72.665 cm²

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