1.
[tex]a=3m\\H=7cm[/tex]
[tex]S=2a^2+4aH\\S=2*(3cm)^2+4(3cm*7cm)=2*9cm^2+4*21cm^2=18cm^2+84cm^2=102cm^2\\V=a^2H\\V=(3cm)^2*7cm=9cm^2*7cm=63cm^3[/tex]
2.
[tex]d_B=6cm\\d_L=10cm[/tex]
[tex]a=\cfrac{d_B}{\sqrt{2}}=\cfrac{6cm}{\sqrt{2}}=3\sqrt{2}cm\\H=\sqrt{{d_L}^2-a^2}=\sqrt{\left(10cm\right)^2-\left(3\sqrt{2}cm\right)^2}=\sqrt{100cm^2-18cm^2}=\sqrt{82}cm\\S=2a^2+4aH=2(3\sqrt{2}cm)^2+4(3\sqrt{2}cm*\sqrt{82}cm)=\\=2*9cm^2+4*6\sqrt{164}cm^2=18cm^2+48\sqrt{41}cm^2=(18+48\sqrt{41})cm^2[/tex]
3.
[tex]d=6cm\\\measuredangle\langle d,B\rangle=30^\circ\\S_B=24cm^2[/tex]
[tex]\measuredangle\langle d,B\rangle=30^\circ\implies H=2d\text{ (trojkat 30-60-90)}\\H=2*6cm=12cm\\V=S_BH=24cm^2*12cm=288cm^3[/tex]
