Question

URGENTE POR FAVOR

Se HGE é um triângulo, onde GE= 40 cm, HE=30 cm, e HG=26 cm. Encontre a área de HGE dando a resposta em centímetro quadrado com duas casas decimais.

Answer 1

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$\Large\boxed{\sf{\underline{F\acute ormula~de~Hier\tilde ao}}}\\\sf A=\sqrt{p\cdot(p-a)\cdot(p-b)\cdot(p-c)}\\\boxed{\begin{array}{c}\sf{p=\dfrac{a+b+c}{2}\longrightarrow p~\acute e~semiper\acute imetro}\\\sf a,b~e~~c~s\tilde ao~lados~do~tri\hat angulo\end{array}}$

$\sf p=\dfrac{40+30+26}{2}\\\sf p=\dfrac{96}{2}\\\sf p=48~cm\\\sf A_{\triangle}=\sqrt{48\cdot(48-40)\cdot(48-30)\cdot(48-26)}\\\sf A_{\triangle}=\sqrt{48\cdot8\cdot18\cdot22}\\\sf A_{\triangle}=\sqrt{16\cdot3\cdot4\cdot2\cdot9\cdot2\cdot2\cdot11}\\\sf A_{\triangle}=\sqrt{16\cdot3\cdot4\cdot4\cdot9\cdot11}\\\sf A_{\triangle}=4\cdot2\cdot2\cdot3\sqrt{33}\\\sf A_{\triangle}=48\sqrt{33}\\\sf A_{\triangle}=48\cdot5,74\\\huge\boxed{\boxed{\boxed{\boxed{\sf A_{\triangle}=275,52~cm^2}}}}$