Question

How many times greater green area than blue are

Answer 1

$Let \: the \: radius \:of \: a \: blue \: semicircle \\be \: \pink {r}$

$\blue{i)Area \: of \: 3 \: blue \:semicircles (A_{1})}\\ = 3 \times \frac{\pi r^{2}}{2}\\= \frac{3\pi r^{2}}{2} \: --(1)$

$ii ) Radius \:of \:the \:big\: semicircle \\= 1\frac{1}{2} r \\= \frac{3r}{2}$

$Area \: of \: the \: big \: semicircle = \pi \frac{\big(\frac{3r}{2}\big)^{2}}{2} \\= \frac{9 \pi r^{2} }{8} \: --(2)$

$iii)\green{ Area \:of \: the \:green \: region (A_{2})}\\= (1) - (2) \\= \frac{3 \pi r^{2} }{2} - \frac{9\pi r^{2}}{8} \\= \frac{12 \pi r^{2} - 9\pi r^{2}}{8} \\= \frac{3\pi r^{2}}{8} \\= \frac{1}{4} \times \Big(\frac{3\pi r^{2}}{2}\Big) \\= \frac{1}{4} \times A_{1}$

$\implies 4 A_{2} = A_{1}$

$\implies 4 \times \green{ (green \:area )} = \blue { blue \:area }$

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Answer 2

Answer:

2 Times see attached screenshot