# 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.

Result

S =  64.952 cm2
S2 =  13.588 cm2

#### Solution:

$a=5 \ \text{cm} \ \\ \ \\ S=\dfrac{ 3 }{ 2 } \cdot \ \sqrt{ 3 } \cdot \ a^2=\dfrac{ 3 }{ 2 } \cdot \ \sqrt{ 3 } \cdot \ 5^2 \doteq 64.9519 \doteq 64.952 \ \text{cm}^2$
$r=a=5 \ \text{cm} \ \\ \ \\ S_{2}=\pi \cdot \ r^2-S=3.1416 \cdot \ 5^2-64.9519 \doteq 13.5878 \doteq 13.588 \ \text{cm}^2$

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