How do you use Heron's formula to determine the area of a triangle with sides of that are 5, 6, and 3 units in length?

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Answer 1 · 2016-01-25T05:28:55

#Area=2sqrt14# square units

#Area=7.48331# square units

The Heron's formula to determine the area of a triangle is:

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

where #s=1/2(a+b+c)#

#s# is one-half of the perimeter of the triangle.

To compute for the area of the triangle using the Heron's Formula, the #s# should be computed first.

Since the given sides are #a=5#, #b=6#, and #c=3#.

#s=1/2*(5+6+3)=7#

#s=7#

Compute the Area after computing s:

#Area=sqrt(7(7-5)(7-6)(7-3))#

#Area=sqrt(7(2)(1)(4))#

#Area=2sqrt(14)#

#Area=7.48331# square units

Have a nice day!!! from the Philippines ....

Answer 2 · 2018-06-15T23:50:23

There's always a better alternative than Heron's Formula. Area #S# satisfies

#16S^2 = (a+b+c)(-a+b+c)(a-b+c)(a+b-c)=(5+6+3)(-5+6+3)(5-6+3)(5+6-3)=14(4)(2)(8)# or

#S=2 sqrt{14}.#