How do you use Heron's formula to determine the area of a triangle with sides of that are 4, 6, and 3 units in length?

1 Answer
Alan P.
Apr 27, 2016

"Area"_triangle~~5.3 sq.units
(see below for use of Heron's formula)

Explanation:

Heron's formula tells us how to calculate the area of a triangle given the lengths of it's three sides.

If (for the general case) the lengths of the three sides are a, b, and c and the semi-perimeter is s=(a+b+c)/2

Then
color(white)("XXX")"Area"_triangle=sqrt(s(s-a)(s-b)(s-c))

For the given triangle with sides 4, 6, and 3
color(white)("XXX")s=13/2
and
color(white)("XXX")"Area"_triangle = sqrt((13/2)(13/2-4)(13/2-6)(13/2-3))

color(white)("XXXXXXX")=sqrt(13/2xx5/2xx1/2xx7/2)

color(white)("XXXXXXX")=sqrt(455)/4

color(white)("XXXXXXX")~~5.3 sq.units

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