Question

Um prisma triangular tem altura de 4 cm e volume de 36 3 cm³. Calcular o valor da ARESTA DA BASE E DA ÁREA TOTAL deste sólido.

Answer 1

$\sf{V=B\cdot H}\\\sf{B\cdot4=363}\\\sf{B=\dfrac{363}{4}}\\\sf{B=90,75~cm^2}$

$\sf{B=\dfrac{\ell^2\sqrt{3}}{4}}\\\sf{\ell^2\sqrt{3}=4\cdot90,75}\\\sf{\ell^2=\dfrac{363}{\sqrt{3}}}\\\sf{\ell^2=\dfrac{363\sqrt{3}}{3}}\\\sf{\ell^2=121\sqrt{3}}\\\sf{\ell=\sqrt{121\sqrt{3}}}\\\huge\boxed{\boxed{\boxed{\boxed{\ell=11\sqrt[4]{3}~cm}}}}$