Question

Apotema unui hexagon regulat este egala cu 3 cm. Determina aria si perimetrul acestui hexagon​

Answer 1

Răspuns:

a=3 cm

A=?

P=?

A=3R²√3/2

a=R√3/2

P=6l

l=R

a=R√3/2 => 3=R√3/2 => R=2√3

A=3R²√3/2 => A=3×(2√3)²√3/2 => A=18√3

l=R => l=2√3

P=6l => P=6×2√3 => P=12√3

Answer 2

$\it \ell_6=R,\ \ \ a_6=\dfrac{\ell\sqrt3}{2}=3 \Rightarrow \dfrac{\ell\sqrt3}{2}=\sqrt3\cdot\sqrt3|_{:\sqrt3} \Rightarrow \dfrac{\ell}{2}=\sqrt3 \Rightarrow \ell=2\sqrt3\ cm\\ \\ \\ \mathcal{P}=6\cdot \ell=6\cdot2\sqrt3=12\sqrt3\ cm\\ \\ \mathcal{A}=6 \cdot\dfrac{\ell \cdot a_6}{2}=3\cdot2\sqrt3\cdot3=18\sqrt3\ cm^2$