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'Maximised Area' printed from https://nrich.maths.org/
Answer:
The large circles could have any radius and the answer will still be the same.
Choose a nice radius for the large circles, e.g. 1 unit
A:
=
$-$
Area = $\pi\times1^2$ $ - $ $2\times\left(\pi\times\left(\frac12\right)^2\right)$
= $\pi$ $-$ $\frac12\pi$ = $\frac12\pi = 1.571$
B:
=
$\times3$
Area of a triangle is $\frac12ab\sin{C} = \frac12\times1\times1\times\sin{120} = \frac{\sqrt3} 4 = 0.433$
Total area is $\frac{3\sqrt3}4 = 1.299$
C:
=
$-$
Area $=4 - \pi = 0.858$
D:
=
Area = 1
E:
=
$-$
$\times4$
= $\pi$ $-$ $\frac12(1\times1 )\times4 =\pi-2 = 1.142$