Given: AB+BC=7.1cm BC+CA=12.1cm CA+AB=7.2cm Calculation: Let the sides of the triangle be: AB=a BC=b CA=c We are given the following system of equations: a+b=7.1 b+c=12.1 c+a=7.2 (a+b)+(b+c)+(c+a)=7.1+12.1+7.2 2a+2b+2c=26.4 a+b+c=13.2 c=13.2−7.1=6.1 a=13.2−12.1=1.1 b=13.2−7.2=6.0 Heron's formula for the area of a triangle is given by: Area =√s(s−a)(s−b)(s−c) Where s is the semi-perimeter of the triangle, given by: s=
a+b+c
2
=
1.1+6.0+6.1
2
=
13.2
2
=6.6cm Area =√6.6(6.6−1.1)(6.6−6.0)(6.6−6.1) Area =√6.6×5.5×0.6×0.5 Area =√6.6×5.5×0.3 Area =√10.89 Area =3.3cm2
