Respuesta :

first find half of perimeter and name it p.
9+6+12=15+12=27
p=27/2=13.5
use this formula
[tex] \sqrt{p(p-a)(p-b)(p-c)} [/tex]
√13.5*4.5*7.5*1.5=2.25*√9*√3*√5=6.75√15
JeanaShupp

Answer: [tex]26.14\text{ mm}^2[/tex]

Step-by-step explanation:

By Heron's formula ,the area of a triangle is given by :-

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex] , where s is semi-perimeter of triangle and a,b ,c are the sides of the triangle.

Given : a=9 mm, b=6 mm, and c=12 mm.

Then , semi-perimeter:[tex]s=\dfrac{a+b+c}{2}[/tex]

[tex]s=\dfrac{9+6+12}{2}=13.5[/tex]

Now, the area of triangle will be :-

[tex]A=\sqrt{13.5(13.5-9)(13.5-6)(13.5-12)}\\\\\Rightarrow\ A=\sqrt{13.5\cdot4.5\cdot7.5\cdot1.5}\\\\\Rightarrow\ A=26.1426375869\text{\ mm}^2\approx26.14\text{ mm}^2[/tex]