Company logo

The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?

Result

S =  18.265 cm2

Solution:

r=4 cm u=2⋅ r=2⋅ 4=8 cm D=u=8 cm  D2=a2+a2  a=D/2=8/2≐4 2 cm≐5.6569 cm  S1=π⋅ r2=3.1416⋅ 42≐50.2655 cm2 S2=a2=5.65692=32 cm2  S=S1−S2=50.2655−32≐18.2655≐18.265 cm2r=4 \ \text{cm} \ \\ u=2 \cdot \ r=2 \cdot \ 4=8 \ \text{cm} \ \\ D=u=8 \ \text{cm} \ \\ \ \\ D^2=a^2+a^2 \ \\ \ \\ a=D / \sqrt{ 2 }=8 / \sqrt{ 2 } \doteq 4 \ \sqrt{ 2 } \ \text{cm} \doteq 5.6569 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ r ^2=3.1416 \cdot \ 4 ^2 \doteq 50.2655 \ \text{cm}^2 \ \\ S_{2}=a^2=5.6569^2=32 \ \text{cm}^2 \ \\ \ \\ S=S_{1}-S_{2}=50.2655-32 \doteq 18.2655 \doteq 18.265 \ \text{cm}^2

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