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Math Help - The height of a pyramid

  1. #1
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    The height of a pyramid

    The square base of a regular pyramid has a side length of 4. Each of the other 4 faces of the pyramid is a triangle with a base of 4 and a height of 6. The pyramid has a total surface area of 64. A second regular pyramid has a square base that is 4 by 4 but its total sure area is double that of the first pyramid. What is the height of each of the triangular faces of the second pyramid?

    I know that the answer is 14, but is there a way to find this without knowing the formula (1/2 (p)(l) + B = TSA)? It's a practice standardized test question
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  2. #2
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    Re: The height of a pyramid

    You have one square + 4 triangles that make the surface area.

    L^2 + 4 \times \frac{1}{2} \times b \times h = 128

    We know the information about the base which is also the length of the square so

    4^2 + 4 \times \frac{1}{2} \times 4 \times h = 128

    16 + 8 \times h = 128

    solve for h
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