d - przekątna
a - krawędź podstawy
[tex]d = a \sqrt{2} [/tex]
[tex]2 \sqrt{5} = a \sqrt{2} | \times \sqrt{2} [/tex]
[tex]2a = 2 \sqrt{10} | \div 2[/tex]
[tex]a = \sqrt{10} [/tex]
[tex]pp = {a}^{2} = {( \sqrt{10}) }^{2} = 10[/tex]
[tex]pb = a \times b = \sqrt{10} \times 8 = 8 \sqrt{10} [/tex]
[tex]pc = 2pp + 4pb = 2 \times 10 + 4 \times 8 \sqrt{10} = 20 + 32 \sqrt{10} = 4(5 + 8 \sqrt{10})[/tex]
