Company logo

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

Correct answer:

S =  18.2655 cm²

Step-by-step explanation:

$$\begin{gathered} r=4\text{cm} \\ u=2\cdot r=2\cdot 4=8\text{cm} \\ D=u=8\text{cm} \\ {D}^2=a^2+a^2 \\ {D}^2=2a^2 \\ D=\sqrt{2}a \\ a=D/\sqrt{2}=8/\sqrt{2}=4\sqrt{2}\text{cm}\doteq 5.6569\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 4^2\doteq 50.2655{\text{cm}}^2 \\ {S}_2=a^2=5.6569^2=32{\text{cm}}^2 \\ S=S_1-S_2=50.2655-32=18.2655{\text{cm}}^2 \end{gathered}$$

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