Question

Find the area of a
hexagonal park of
side 100 m, if O in
the figure represents
the centre of the park
and OM = 503 m.
50 V3 m​

Answer 1

The area of a  hexagonal park =  15000$\sqrt{3}$ $m^{2}$

Step-by-step explanation:

Given,

The side of a  hexagonal park (a) = 100 m

To find, the area of a  hexagonal park = ?

We know that,

The area of a hexagon = 6 × Area of equilateral triangle

= 6 × $\dfrac{\sqrt{3} }{4} a^2$

= 6 ×$\dfrac{\sqrt{3}}{4} (100)^2$

= 6 × $\dfrac{\sqrt{3}}{4} 100\times 100$

= 6 × $\sqrt{3}}\times 25\times 100$

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

Thus, the area of a  hexagonal park =  15000$\sqrt{3}$ $m^{2}$