Question

find the area of a regular hexagon of side is 8 cm​

Answer 1

Answer:

Area ≈166.28

Step-by-step explanation:

As shown in the picture.

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Answer 2

$\; \star \; {\underline{\boxed{\pmb{\orange{\frak{ \; Given \; :- }}}}}}$

• ➺ Side = 8cm

$\begin{gathered}\begin{gathered} \\ \\ \end{gathered} \end{gathered}$

$\; \star \; {\underline{\boxed{\pmb{\red{\frak{ \; To \; Find \; :- }}}}}}$

• ➺ Area of hexagon = ?

$\begin{gathered}\begin{gathered} \\ \\ \qquad{\rule{200pt}{2pt}} \end{gathered}\end{gathered}$

$\; \star \; {\underline{\boxed{\pmb{\purple{\frak{ \; SolutioN \; :- }}}}}}$

$❒ {\underline{\underline{\sf{ \; Formula \; Used \; :- }}}}$

${\; \longrightarrow \; {\underline{\boxed{\sf{Area_{(Hexagon)} = \dfrac{3 \sqrt{3}a }{2}a {}^{2} }}}} \; \red\bigstar }$

$\begin{gathered}\begin{gathered} \\ \end{gathered}\end{gathered}$

$❒ {\underline{\underline{\sf{ \; Calculating \; the \; Area\; :- }}}}$

${\; \longrightarrow \; {\sf{Area_{(Hexagon)} = \dfrac{3 \sqrt{3}a }{2}a {}^{2} }} \; }$

${\; \longrightarrow \; {\sf{Area_{(Hexagon)} = \dfrac{3 \sqrt{3} }{2} \times 8 {}^{2} }} \; }$

${\; \longrightarrow \; {\sf{Area_{(Hexagon)} = \dfrac{3 \sqrt{3} }{2} \times64 }} \; }$

${\; \longrightarrow \; {\sf{Area_{(Hexagon)} = \dfrac{192\sqrt{3} }{2} }} \; }$

${\; \longrightarrow \; {\sf{Area_{(Hexagon)} = \dfrac{ \cancel{192}\sqrt{3} }{ \cancel2} }} \; }$

$\begin{gathered}\begin{gathered} \; \longmapsto \; {\underline{\boxed{ \frak{\pink{Area_{(Hexagon)} = 96 \sqrt{3} }}}}} \; \bigstar \\ \\ \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered} \\ \\ \end{gathered} \end{gathered}$

$\qquad$ ∴ The area of the hexagon is $\sf{9 6\sqrt{3} }$

$\begin{gathered}\begin{gathered} \\ {\underline{\rule{300pt}{9pt}}} \end{gathered} \end{gathered}$