Square and circles

The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.

Correct result:

S1 =  242.92 cm2
S2 =  200 cm2

Solution:

a=20 cm S=a2=202=400 cm2 r=a/2=20/2=10 cm K=π r2=3.1416 102314.1593 cm2  S1=S2 K/4=4002 314.1593/4=242.92 cm2
O=SK4=400314.1593421.4602 cm2 S2=S12 O=242.92042 21.4602=200 cm2



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