Question

Find the area of shaded portion​

Answer 1

Answer:

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Step-by-step explanation:

$to \: find = \\ area \: of \: shaded \: region \\ \\ so \: here \: radius \: of \: circle \: (r) = 14.cm \\ thus \: diameter \: = 2 \times 14 = 28.cm \\ \\ so \: we \: know \: that \\ area \: of \: circle = \pi.r {}^{2} \\ = \frac{22}{7} \times (14) {}^{2} \\ \\ = \frac{22}{7} \times 14 \times 14 \\ \\ = 22 \times 2 \times 14 \\ = 44 \times 14 \\ = 616.cm {}^{2} \: \: \: \: (1)$

$so \: the \: diameter \: of \: circle \: would \: be \: \\ diagonal \: of \:inscribed \: square \: \\ thus \: we \: know \: that \\ \\ diagonal \: of \: square = \sqrt{2} .side \: of \: square \\ \\ ie \: 28 = \sqrt{2} .side \\ ie \: side = \frac{28}{ \sqrt{2} } \\ \\ rationalising \: denominator \\ we \: get \\ = \frac{28}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ \\ = \frac{28 \sqrt{2} }{2} \\ = 14 \sqrt{2} \\ \\ hence \: then\\ \: side \: of \: inscribed \: square \: (s) = 14 \sqrt{2} .cm$

$now \: using \: \\ area \: of \: square = side {}^{2} \\ = (14 \sqrt{2} ) {}^{2} \\ = 196 \times 2 \\ = 392.cm {}^{2} \: \: \: \: \: \: \: (2)$

$so \: thus \: \\ area \: of \: shaded \: region = area \: of \: circle - area \: of \: inscribed \: square \\ = 616 - 392 \: \: \: \: \: \: \: from \: (1) \: and \: (2) \\ \\ = 224.cm {}^{2} \\ \\ hence \: area \: of \: shaded \: region \: is \: 224.cm {}^{2}$

Answer 2

QUESTION:-

Find the area of the shaded region:-

EXPLANATION:-

The figure in enclosed in the circle is square (as it's all side are equal)

SO let's find the are of this square:-

The diagonal of the square will 14+14

Diagonal=28 m

We know that the relation between square diagonal and it's side is:-

(side)²+(side)²=(diagonal)²

Diagonal=28 m

(side)²+(side)²=(28)²

2(side)²=784

(side)²=784/2

(side)²=392

side=√392

side≈20 m

So the side of the square is20 m(approx)

So the area will be:-

→side²

→20²

→400 m²

Now let's find the area of circle:-

area=Пr²

r=14

Area=22/7×(14)²

Area=616 m²

So area of shaded portion is :-

→616-400

→216

SO area of shaded portion is 216 m²