Consider R as the radius of each circle. Divide the figure in 4 quarters.

In any quarter: the blue area is a quarter of disc (pi*R²/4) from which we remove a blank part, which is the small square size R² minus the same quarter of disc. So this petal has an area of (pi*R²/4 - (R² - pi*R²/4)) = R² (2*pi/4 - 1) = R²/4 (2*pi - 4)

Now for the 4 petals, multiply by four: A = R² (2*pi - 4)

For a big square of side 20 cm, R=10 cm thus area is 100*(2*pi - 4) = (200*pi - 400) cm², around 228,32 cm²

228 cm² if you take pi=3,14