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Find the area of a circle circumscribed about a regular hexagon with an apothem of 5 inches. Round to the nearest tenth

  • Geometry -

    I am not certain of your comfort with this, however, knowing either the apotherm or the circumradius you can find the other.

    circumradius * cos(180/n)=apotherm

    so in this case, atotherm=5inches, n=6

    so circumradius * cos(30)=5inches
    radius= 5inches / .866

    Now the area of the circumscribed circle is PI*radius^2

    Neat stuff. Thank your teacher.

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