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Math Help - Show that the volume of a pyramid of height h whose base is an equilateral triangle o

  1. #1
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    Show that the volume of a pyramid of height h whose base is an equilateral triangle o

    Show that the volume of a pyramid of height h whose base is an equilateral triangle of side s is equal to
    {(√3)(h)(s^2)}
    (12)
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  2. #2
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    Quote Originally Posted by derrickd View Post
    Show that the volume of a pyramid of height h whose base is an equilateral triangle of side s is equal to
    {(√3)(h)(s^2)}
    (12)
    For, equilateral triangle of base,

    height of equilateral triangle = \sqrt{s^2-\left(\frac{s}{2}\right)^2}=\frac{s\sqrt{3}}{2}

    Area of equilateral triangle (base) A= \frac{s\times \frac{s\sqrt{3}}{2}}{2}=\frac{s^2\sqrt{3}}{4}

    Volume= \frac{A\times h}{3}=\frac{\frac{s^2\sqrt{3}}{4}h}{3}=\frac{hs^2\  sqrt{3}}{12}
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