find the are of a regular octagon whose sides are 12cm long.

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  1. cut the octogon into 8 congruent triangles, with vertices at the centre of the octogon.

    Consider one of those triangles.
    It will have a base of 12 cm, and the angle across from the 12 will be 45º, with the other two angles 67.5º each.
    Let its height be h.
    tan 67.5 = h/6
    h = 14.485

    so the area of that triangle is 1/2(12)(14.485
    = 86.912

    so the octogon is 8(86.912) = 695.29 cm^2

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