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Compute the area of a triangle with sides.

15 × 15 × 18

a = How many square units?

  • Geometry -

    There is a formula for the area of a triangle in terms of the side lengths.

    Don't ask me to derive it. Here it is:

    Let s = (a +b +c)/2
    a,b and c are the side lengths.
    For your triangle, s = 24

    Area = sqrt[s*(s-a)*(s-b)*(s-c)]
    = sqrt[24*9*9*6) = 108 square units

    Check: Your triangle is isosceles and if you drop a line from the apex to the middle of the base, you have two
    9:12:15 right triangles. The area of each is (1/2)(9*12) and that makes a total area of 108.

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