Question

Considere o triângulo equilátero DEF

a) Calcule o comprimento h da altura DH

b) Calcule a área do triângulo DEF

Answer 1

Resposta:

Explicação passo a passo:

$a)HF=\frac{l}{2} \\\\h^2+(\frac{l}{2} )^2=l^2\\\\h^2+\frac{l^2}{4}=l^2\\\\4h^2+l^2=4l^2 \\\\4h^2=4l^2-l^2\\\\4h^2=3l^2\\\\h^2=\frac{3l^2}{4} \\\\h=\frac{l\sqrt{3} }{2}$

$b)A=\frac{bh}{2}\\\\A=\frac{l.\frac{l\sqrt{3} }{2} }{2}\\\\A=\frac{\frac{l^2\sqrt{3} }{2} }{2}\\\\A=\frac{l^2\sqrt{3} }{4}$