Answer:
31.9 cm² (3 s.f.)
Step-by-step explanation:
[tex]\boxed{area \: of \: sector = \frac{θ}{360º} \times \pi {r}^{2} }[/tex]
∠AOD
= 360° -60° - 120° -45° (∠s at a pt.)
= 135°
Area of shape
[tex] = \frac{60°}{360°} (\pi)({2}^{2}) + \frac{120°}{360°} (\pi)(3^{2} )+ \frac{45°}{360°}(\pi)( 5 {}^{2}) + \frac{135°}{360°} (\pi)(3 {}^{2} )[/tex]
[tex] = \frac{1}{6} (4\pi) + \frac{1}{3} (9\pi) + \frac{1}{8} (25\pi) + \frac{3}{8} (9\pi)[/tex]
[tex] = \frac{4}{6} \pi + \frac{9}{3} \pi + \frac{25}{8} \pi + \frac{27}{8} \pi[/tex]
[tex] = \frac{61}{6} \pi[/tex]
= 31.9 cm² (3 s.f.)
