5. Rysunek pomocniczy w zalacznikach
[tex]\alpha = 30\\Pp = a^2\\d = a\sqrt2\\\frac12d=\frac{a\sqrt2}2\\tg\alpha = \frac{H}{\frac{a\sqrt2}2}\\tg\alpha = H:\frac{a\sqrt2}2\\tg\alpha=H*\frac{2}{a\sqrt2}\\tg\alpha=H*\frac{2\sqrt2}{2a}\\tg\alpha=H*\frac{\sqrt2}{a}\\\frac{\sqrt3}3=H*\frac{\sqrt2}{a} /*\frac{a}{\sqrt2}\\\frac{\sqrt3}3*\frac{a}{\sqrt2}=H\\H=\frac{a\sqrt3}{3\sqrt2} * \frac{\sqrt2}{\sqrt2}\\H=\frac{a\sqrt6}{3*2}\\H=\frac{a\sqrt6}{6}\\V = Pp * H\\V = a^2*\frac{a\sqrt6}{6}\\V=\frac{a^3\sqrt6}{6}[/tex]
6. Rysunek pomocniczy w zalacznikach
[tex]Ob = 4a\\20cm=4a /:4\\5cm=a\\e = 6cm\\\frac12e=3cm\\a^2=(\frac12e)^2+(\frac12f)^2\\(5cm)^2=(3cm)^2+(\frac12f)^2\\25cm^2=9cm^2+(\frac12f)^2\\25cm^2-9cm^2=(\frac12f)^2\\16cm^2=(\frac12f)^2\\\frac12f=\sqrt{16cm^2}\\\frac12f=4cm /*2\\f=8cm\\P=\frac{ef}{2}\\P=\frac{6cm*8cm}{2}\\P=6cm*4cm=24cm^2\\P = ah\\24cm^2=5cm*h /:(5cm)\\\frac{24cm^2}{5cm}=h\\h=4\frac45cm = 4\frac8{10}cm\\h=4,8cm[/tex]
