Question

find the area of a hexagonal park of side 100 m, if O in the figure represent the center of the park and OM=50√3.​

Answer 1

$\red{\textbf{Answer :-}}$$= 15000 \sqrt{3}{m}^{2}$

Step-by-step explanation:

$\red{\textbf{Given :-}}$

$\textsf{side = 100 m}$

AB = BC =CD=DE=EF = AF = 100m

$OM = 50 \sqrt{3 \: } \: m$

$\red{\textbf{To find :-}}$

$\textsf{Area of hexagonal park.}$

$\textsf{According to the question, }$

$\red{\textbf{Area of hexagon=}}$

6 ×$\textsf{Area of equilateral triangle }$

$so, \: area \: of \: hexagonal \: park$,

6 ×$\LARGE \frac{\sqrt{3} \: \: }{4} \small {a}^{2}$

6 ×$\LARGE\frac{\sqrt{3} }{4}\small (100 {)}^{2}$

6 ×$\LARGE\frac{ \sqrt{3} }{4} \: \: \small 100 * 100$

$= 15000 \sqrt{3}{m}^{2}$

$\textsf{So, Area of the hexagonal park }$$= 15000 \sqrt{3}{m}^{2}$