Respuesta :

The area of 1/2 the hexagon is
.. A = (1/2)*(1/2)*6*(10 cm)*x = 15x
.. 130 cm^2/15 = x ≈ 8.7 cm

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In a regular hexagon, the apothem is always the side length multiplied by (√3)/2. It will be 8.7 cm regardless of the shading.