6 regular polygon

A regular six-sided polygon has a side 5 cm long. Calculate its area. Compare how many more cm² (square centimeters) has a circle inscribed the 6-gon.

Correct answer:

S =  64.9519 cm²
S₂ =  13.5879 cm²

Step-by-step explanation:

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

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

Try another example