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Thread: [RESOLVED] Calculate surface area of pyramid

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    eXtreme Programmer .paul.'s Avatar
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    Resolved [RESOLVED] Calculate surface area of pyramid

    How can I calculate the surface area of a regular 4 sided pyramid, using base length and overall height (not slant height)?

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    Only Slightly Obsessive jemidiah's Avatar
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    Re: Calculate surface area of pyramid

    To find the height of the four isosceles triangles, draw a right triangle from the vertex to the center of the base to the midpoint of one of the sides. If the sides have length A and the overall height is H, then the Pythagorean Theorem says this right triangle's hypotenuse is sqrt(H^2 + (A/2)^2). The area of each isosceles triangle is then 1/2 * sqrt(H^2 + (A/2)^2) * A, so the overall area is four times this plus the base area, namely

    A^2 + 2A sqrt(H^2 + A^2/4)
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    eXtreme Programmer .paul.'s Avatar
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    Re: Calculate surface area of pyramid

    Thanks. That worked well...

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    eXtreme Programmer .paul.'s Avatar
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    Re: [RESOLVED] Calculate surface area of pyramid

    Can't rate you this time. Gotta spread some ratings...

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