Respuesta :

Answer:

38

Step-by-step explanation:

Answer:

[tex]32.62\:\mathrm{cm^2}[/tex]

Step-by-step explanation:

The area of a triangle with side lengths [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] is given by:

Let [tex]s=\frac{a+b+c}{2}[/tex] (semi-perimeter)

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

We're given three side lengths with lengths 15 cm, 18 cm, and 5 cm. Therefore, the semi-perimeter, [tex]s[/tex], is equal to [tex]\frac{15+18+5}{2}=\frac{38}{2}=19[/tex].

Thus, the area of this triangle is:

[tex]A=\sqrt{19(19-18)(19-15)(19-5)},\\A=\sqrt{19\cdot 1\cdot 4\cdot 14},A=\sqrt{1064}=32.6190128606\approx \boxed{32.62\:\mathrm{cm^2}}[/tex]