# Quatrefoil

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

Result

S =  20.549 cm2

#### Solution:

$a = 6 \ cm \ \\ r = a/2 = 6/2 = 3 \ cm \ \\ S_{ 1 } = \pi \cdot \ r^2/4 = 3.1416 \cdot \ 3^2/4 \doteq 7.0686 \ cm^2 \ \\ S_{ 2 } = 2 \cdot \ S_{ 1 } - r^2 = 2 \cdot \ 7.0686 - 3^2 \doteq 5.1372 \ cm^2 \ \\ S = 4 \cdot \ S_{ 2 } = 4 \cdot \ 5.1372 \doteq 20.5487 = 20.549 \ cm^2$

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