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Geometry

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*These are regular polygons*
1.Find the area of a triangle with an apothem of 8 inches.
2.Find the area of a square with a radius of 12 inches.
3.Find the area of a pentagon with a hypotenuse of 10 inches.

  • Geometry -

    1. To be speaking of an "apothem" of a triangle, the triangle must be equilateral.
    The apothem is the distance from the centre (centroid) to a side, and the apothem must be 1/3 of the length of the median
    so the median is 24 inches, which makes the height 24 inches.
    then by knowing the ratio of sides of the 30-60-90 triangle, the side must be 48/√3
    area = (1/2)(48/√3)(24) = 576/√3 square inches

    2. We don't speak of a square having a radius.
    Did you mean diameter?
    if so let each side of square be x
    x^2 + x^2 = 12^2
    x = √98 =
    area = x^2 = 98

    3. Again, where does a hypotenuse come from in a pentagon?
    Did you mean diagonal?
    Find the internal angle. (you should get 108°)
    From that you should be able to find all kinds of angles, depending on which lines you sketch.

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