Use Heron's Formula to find the area of a triangle with sides of 5, 12, and 16 cm ?

I am desperate for help.

Please show all working out so I know how to do it.

Thanks.

7 Answers

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  • 1 decade ago
    Favorite Answer

    Heron's (or Hero's) formula for the area, A, of a triangle is

    A = sqrt(s(s-a)(s-b)(s-c))

    where a, b and c are the lengths of the sides and s = (a + b + c) / 2.

    For your triangle, s = (5 + 12 + 16) / 2 = 16.5, so

    A = sqrt(16.5 x 11.5 x 4.5 x 0.5) = 20.66 approx.

    Isn't this a beautiful formula?

    Source(s): E.J. Borowski and J.M. Borwein, Collins Dictionary of Mathematics. London: HarperCollins, 1989.
  • Anonymous
    4 years ago

    it is a top triangle, with 20 cm area because of the fact the hypotenuse, meaning you will locate the area utilising the measures of the different 2 facets. in the different case you need to use the Heron's formula: sq. root of s(s-a)(s-b)(s-c) the place s is a semiperimeter (this is the sum of the three facets divided via 2) and a, b, c are the measures of the three facets.

  • 1 decade ago

    Heron's formula can be derived from the properties of triangles.

    Area = sqrt s(s-a)(s-b)(s-c)

    where s = semi perimeter = (a+b+c)/2

  • 1 decade ago

    Here

    a = 5

    b = 12

    c = 13

    s = (a + b + c)/2 = 15

    Heron's formula -

    A = sq. rt. s (s - a) (s - b) (s - c) = sq rt. 900

    A = 30 cm^2

    Hope this helps.

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  • 1 decade ago

    960 cm

  • 1 decade ago

    Here you go bud. Nice and clear!!

    http://en.wikipedia.org/wiki/Heron's_formula

  • Anonymous
    1 decade ago

    Area = sqrt( s(s - a)(s - b)(s - c) ) where s = (1/2)(a + b + c).

    s = 16.5

    s - a = 11.5

    s - b = 4.5

    s - c = 0.5

    Area = sqrt(16.5 * 11.5 * 4.5 * 0.5)

    = 20.66cm^2.

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