6 regular polygon

It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm² (square centimeters) has a circle in which is inscribed the 6-gon.

Correct result:

S =  64.9519 cm²
S₂ =  13.5879 cm²

Solution:

$$\begin{gathered} a=5\text{ cm } \\ S={\displaystyle \frac{3}{2}}\cdot \sqrt{3}\cdot a^2={\displaystyle \frac{3}{2}}\cdot \sqrt{3}\cdot 5^2=64.9519{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} r=a=5=5\text{ cm } \\ {S}_2=\pi \cdot r^2-S=3.1416\cdot 5^2-64.9519=13.5879{\text{cm}}^2 \end{gathered}$$

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