Math (check)

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what is the slant height for the given pyramid to the nearest whole unit? with a pyramid base of 12cm and a height of 8cm. MY ANSWER: 14

  • Math (check) -

    Interpretation #1 : Slant height is the edge of the pyramid

    Consider the right-angled (internal) triangle formed by the height , half the diagonal of the base and hypotenuse being the slant height.

    let the slant height be x

    let the diagonal of the base be d
    d^2 = 1^2 + 12^2 = 288
    d^2 = 288
    d = 12√2
    d/2 = 6√2

    then x^2 = (d/2)^2 + 8^2 = 72 + 64 = 136
    x+ √136 = 2√34 or appr 11.66



    Interpretation #2 : slant height is the altitude of one of the triangles:



    Consider one of the triangles whose base runs from the centre of the pyramid to the midpoint of a base side, with height 8 and hypotenuse as your "slant height"
    base = 6
    slant height = hypotenuse = y
    height =8

    where y^2 = 8^2 + 6^2 = 100
    y = √100 = 10



    Check: notice I can obtain the edge length from this as well

    x^2 = y^2 + 6^2
    x^2 = 100+36 = 136
    x = √136 (same as above)

  • Math (check) -

    thank you!

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