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.
- rrabbitLv 41 decade agoFavorite 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.
- Anonymous4 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.
- nayanmangeLv 41 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
- PrashantLv 61 decade ago
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
- Anonymous1 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)