How do you use Heron's formula to find the area of a triangle with sides of lengths 12 12, 6 6, and 8 8?

1 Answer
SagarStudy
Jan 25, 2016

Area=21.33Area=21.33 square units

Explanation:

Heron's formula for finding area of the triangle is given by
Area=sqrt(s(s-a)(s-b)(s-c))Area=√s(s−a)(s−b)(s−c)

Where ss is the semi perimeter and is defined as
s=(a+b+c)/2s=a+b+c2

and a, b, ca,b,c are the lengths of the three sides of the triangle.

Here let a=12, b=6a=12,b=6 and c=8c=8

implies s=(12+6+8)/2=26/2=13⇒s=12+6+82=262=13

implies s=13⇒s=13

implies s-a=13-12=1, s-b=13-6=7 and s-c=13-8=5⇒s−a=13−12=1,s−b=13−6=7ands−c=13−8=5
implies s-a=1, s-b=7 and s-c=5⇒s−a=1,s−b=7ands−c=5

implies Area=sqrt(13*1*7*5)=sqrt455=21.33⇒Area=√13⋅1⋅7⋅5=√455=21.33 square units

implies Area=21.33⇒Area=21.33 square units

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