Verified answer

Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\sf A = \sqrt{p(p - a)(p - b)(p - c)}\rightarrow\textsf{F{\'o}rmula de H{\'e}ron}[/tex]

[tex]\sf p = \dfrac{a + b + c}{2}[/tex]

[tex]\sf p = \dfrac{4 + 3 + 2}{2}[/tex]

[tex]\sf p = \dfrac{9}{2}[/tex]

[tex]\boxed{\sf p = 4,5\:cm}\rightarrow\textsf{semiper{\'i}metro}[/tex]

[tex]\sf A = \sqrt{(4,5)(4,5 - 4)(4,5 - 3)(4,5 - 2)}[/tex]

[tex]\sf A = \sqrt{(4,5)(0,5)(1,5)(2,5)}[/tex]

[tex]\sf A = \sqrt{(4,5)(0,5)(1,5)(2,5)}[/tex]

[tex]\sf A = \sqrt{8,4375}[/tex]

[tex]\boxed{\boxed{\sf A = 2,90\:cm^2}}[/tex]