Question

find the area of shaded region ​

Answer 1

Answer:

Step-by-step explanation:

area of shaded region = area of circle/4 - area of square

area of circle = pie*r*r=22/7*6root2*6root2=226.28

area of quadrant = 226.28/ 4 =56.57

area of square when diagonal is given = 0.5*d*d=0.5 *6root2*6root2=36

area of shaded region= 56.57-36=20.57

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Answer 2

AnswEr:-

Your Answer is 20.52 cm².

ExplanaTion:-

Given:-

• A square PQRS is inscribed in a quadrant BQA.

• Radius of the quadrant (i.e. OQ) = $\tt 6\sqrt{2}cm$.

To Find:-

• The area of shaded region.

Concepts Used:-

• Area of square = S².

• Area of a quadrant,

$\tt = \dfrac{1}{4} \times \pi {r}^{2} .$

$\tt\bullet D = \sqrt{2}\times S.$

Where,

• S = Side of the square.
• D = Diagonal of the square.
• $\tt\pi$ = 3.14

So Here,

Area of shaded region,

$\tt=\: Area \:of \:quadrant - Area\: of \:square.$

Also,

For finding the area of square we need to find out its side.

And in the question OQ which is the diagonal of square Is given as $\tt 6\sqrt{2} \:cm$.

Therefore we know that,

$\tt\longrightarrow D = \sqrt{2}\times S$

$\tt\longrightarrow 6 \cancel{\sqrt{2} }\: cm \: = \cancel{ \sqrt{2} } \times side. \\ \\ \tt\longrightarrow6 \: cm = side \\ \\ \tt\longrightarrow \: side = 6 \: cm$

So the side of the square is 6 cm.

$\tt\therefore$ Area of shaded region

$\tt = ( \dfrac{1}{4} \times 3.14 \times (6 \sqrt{2} \: cm) {}^{2} - [(6 \: cm) {}^{2} ] . \\ \\ \tt = [ \dfrac{1}{4} \times3.14 \times (6 \times 6 \times \sqrt{2} \times \sqrt{2} \: \: cm {}^{2} ] - (36 \: cm {}^{2} ) \\ \\ \tt = [( \dfrac{1}{\cancel4} \times 3.14 \times\cancel {72}) - (36)] \:cm {}^{2} \\ \\ \tt = [(3.14 \times 18) - (36)] \: cm {}^{2} \\ \\ \tt = (56.52 - 36)cm {}^{2} \\ \\ \tt = 20.52 \: cm {}^{2}$

Therefore thebarea of shaded region is 20.52 cm².