Question

Total area of hexagon 480 cm find the length

Answer 1

$13.60 \: cm \: \: \: \: (approx)$

Step-by-step explanation:

$Let, \: \: the \: \: length \: \: of \: \: hexagon = x \\ we \: \: know \: \: \boxed{A \: \: hexagon \: \: is \: \: made \: \: up \: \: of \: \: six \: \: equal \: \: equilateral \: \: triangles} \\ then, \: \: \: area \: \: of \: \:a \: \: hexagon = 6 \times area \: \: of \: \: a \: \: equilateral \: \: triangle \\ Now, \: \: \: putting \: \: values \\ 480 \: {cm}^{2} = 6 \times \frac{ \sqrt{3} {x}^{2} }{4} \\ \: \: \: 480 = \frac{3 \sqrt{3} {x}^{2} }{2} \\ \: \: \: \: \: \: \: {x}^{2} = \frac{480 \times 2}{3 \sqrt{3} } \\ {x}^{2} = \frac{320}{ \sqrt{3} } \\ \: {x}^{2} ≈ \frac{320}{1.73} \\ \: \: \: \: {x}^{2} ≈ 184.97 \\ \: \: \: \: \: \: \: \: \: \: x ≈ \sqrt{184.97} \\ \: \: \: \: \: \: \: \: \: \: \: ≈ \boxed { 13.60}$