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Determine the volume of a triangular prism with sides of the triangular base measuring 10cm, 14 cm, and 21 cm and having height 30 cm.

  • Math -

    That will not work because you do not know the altitude of the triangle. You must get the area of the triangular base from the lengths of the three sides.
    To find the altitude from the 21 cm base:
    call the part next to the 10 cm leg x
    call the part next to the 14 cm leg (21-x)
    call the altitude h
    then
    x^2 + h^2 = 100
    (21-x)^2 + h^2 = 196
    so
    (21-x)^2 -x^2 =96
    441 - 42x = 96
    42 x = 345
    x = 8.214
    x^2 = 67.47
    100-x^2 = 32.5 = h^2
    h = 5.7
    so
    (1/2)h *21 = 59.9 = area of base triangle
    multiply by 30 to get volume

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