Question

Answer this question ...

@Maths aryabhatta
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Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Area\:of\:total\:shaded\:region=252\:cm^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Radius \: of \: circle = 7 \: cm \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Area \: of \: shaded \: region =?$

• According to given question :

$\tt \circ \: Side \: of \: square = 14 \: cm \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: one \: shaded \: region = Area \: of \: square - 4 \times Area \: of \: quadrant \\ \\ \tt: \implies Area \: of \: one \: shaded \: region = {side}^{2} - 4 \times \frac{1}{4} \pi {r}^{2} \\ \\ \tt: \implies Area \: of \: one \: shaded \: region = {14}^{2} - \pi {7}^{2} \\ \\ \tt: \implies Area \: of \: one \: shaded \: region =196 - \frac{22}{7} \times 7 \times 7 \\ \\ \tt: \implies Area \: of \: one \: shaded \: region =196 - 22 \times 7 \\ \\ \tt: \implies Area \: of \: one \: shaded \: region =196 - 154 \\ \\ \green{\tt: \implies Area \: of \: one \: shaded \: region =42 { \: cm}^{2} } \\ \\ \tt \circ \: Total \: shaded \: part = 6 \\ \\ \bold{For \: Total \: shaded \: region : } \\ \tt: \implies Area \: of \:total\: shaded \: region =42 \times 6 \\ \\ \green{\tt: \implies Area \: of \:total \: shaded \: region =252 \: {cm}^{2} }$

Answer 2

We know that, Area of one shaded region = Areaofsquare − 4 × Area of quadrant

⟹ Area of one shaded region = side² −4× 1/4 πr²

⟹ Area of one shaded region = 14² - π (7)²

⟹ Area of one shaded region = 196 - (22×7)

⟹ Area of one shaded region = 196 - 154 = 42 cm²

Now, total number of shaded parts = 6

Therefore, Area of total shaded region = (42×6) cm² = 252 cm² (Ans)