Quatrefoil

Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.

Result

S =  20.549 cm2

Solution:

a=6 cm r=a/2=6/2=3 cm S1=π r2/4=3.1416 32/47.0686 cm2 S2=2 S1r2=2 7.0686325.1372 cm2 S=4 S2=4 5.137220.548720.549 cm2a=6 \ \text{cm} \ \\ r=a/2=6/2=3 \ \text{cm} \ \\ S_{1}=\pi \cdot \ r^2/4=3.1416 \cdot \ 3^2/4 \doteq 7.0686 \ \text{cm}^2 \ \\ S_{2}=2 \cdot \ S_{1} - r^2=2 \cdot \ 7.0686 - 3^2 \doteq 5.1372 \ \text{cm}^2 \ \\ S=4 \cdot \ S_{2}=4 \cdot \ 5.1372 \doteq 20.5487 \doteq 20.549 \ \text{cm}^2



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