Geometry

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The base of a regular pyramid is a hexagon whose sides have length 5 ft. If a lateral edge of this pyramid has length 9 ft, what is the surface area of the pyramid?

  • Geometry -

    The distance from the apex to the middle of a side of the base is
    sqrt(9^2 - 2.5^2) = 8.6458 ft
    That equals the height h of one of the six triangular sides.
    The area of one triangular side is
    (1/2)*b*h = 21.615 ft^2
    Multiply that by 6 for the total side area: 129.7 ft^2

    You did not say if they wanted the area of the base included. That is easy enough to do.

  • Geometry -

    You should be able to do the side triangles the same way I showed you in your other post.

    The problem is the base.
    It is a hexagon.
    It is made up of 6 equilateral triangles.
    For each triangle all sides are equal and all angles are 60°
    Work on only one triangle
    You can find the height by Pythagoras or simple trig
    Then find the area of ONE triangle, then multiply by 6

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