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# 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

- 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
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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- 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)

= 20.66cm^2.