Rodzaj ostrosłupa	Długość krawędzi podstawy	Wysokość ściany bocznej	Pole podstawy  $\left(P_p\right)$	Pole  powierzchni bocznej  $\left(P_b\right)$	Pole powierzchni całkowitej  $\left(P_c\right)$
prawidłowy  czworokątny	$2\text{cm}$	$5\text{cm}$	$4{\text{cm}}^2$	$20{\text{cm}}^2$	$24{\text{cm}}^2$
	$5\text{cm}$	$4\text{cm}$	$25{\text{cm}}^2$	$40{\text{cm}}^2$	$65{\text{cm}}^2$
	$5\text{cm}$	$10\text{cm}$	$25{\text{cm}}^2$	$100{\text{cm}}^2$	$125{\text{cm}}^2$
prawidłowy trójkątny	$1\text{cm}$	$2\text{cm}$	$\frac{\sqrt{3}}{4}{\text{cm}}^2$	$3{\text{cm}}^2$	$\left(\frac{\sqrt{3}}{4}+3\right){\text{cm}}^2$
	$6\text{cm}$	$6\text{cm}$	$9\sqrt{3}{\text{cm}}^2$	$54{\text{cm}}^2$	$\left(9\sqrt{3}+54\right){\text{cm}}^2$
	$2\text{cm}$	$\sqrt{3}\text{cm}$	$\sqrt{3}{\text{cm}}^2$	$3\sqrt{3}{\text{cm}}^2$	$4\sqrt{3}{\text{cm}}^2$
prawidłowy sześciokątny	$3\text{cm}$	$5\text{cm}$	$13\frac{1}{3}\sqrt{3}{\text{cm}}^2$	$45{\text{cm}}^2$	$\left(13\frac{1}{3}\sqrt{3}+45\right){\text{cm}}^2$
	$2\text{cm}$	$7\text{cm}$	$6\sqrt{3}{\text{cm}}^2$	$42{\text{cm}}^2$	$\left(6\sqrt{3}+42\right){\text{cm}}^2$
	$2\text{cm}$	$10\text{cm}$	$6\sqrt{3}{\text{cm}}^2$	$60{\text{cm}}^2$	$\left(6\sqrt{3}+60\right){\text{cm}}^2$

 

$\text{I wiersz tabeli}$  

$P_p=a^2={\left(2\text{cm}\right)}^2=\underline{\underline{4{\text{cm}}^2}}$  

$P_b=4\cdot \frac{1}{2}\cdot 2\text{cm}\cdot 5\text{cm}=\underline{\underline{20{\text{cm}}^2}}$  

$P_c=P_p+P_b=4{\text{cm}}^2+20{\text{cm}}^2=\underline{\underline{24{\text{cm}}^2}}$    

 

$\text{II wiersz tabeli}$  

$a^2=25{\text{cm}}^2\mid \sqrt{}$  

$a=\sqrt{25}\text{cm}=\underline{\underline{5\text{cm}}}$  

$P_b={\sout{4}}^2\cdot \frac{1}{{\sout{2}}^1}\cdot 5\text{cm}\cdot 4\text{cm}=\underline{\underline{40{\text{cm}}^2}}$  

$P_c=25{\text{cm}}^2+40{\text{cm}}^2=\underline{\underline{65{\text{cm}}^2}}$    

 

$\text{III wiersz tabeli}$  

$a^2=25{\text{cm}}^2\mid \sqrt{}$  

$a=\sqrt{25}\text{cm}=\underline{\underline{5\text{cm}}}$  

$P_b=4\cdot \frac{1}{2}\cdot a\cdot h$  

$100{\text{cm}}^2=2\cdot 5\text{cm}\cdot h$  

$100{\text{cm}}^2=10\text{cm}\cdot h\mid :10\text{cm}$  

$h=\underline{\underline{10\text{cm}}}$  

$P_c=25{\text{cm}}^2+100{\text{cm}}^2=\underline{\underline{125{\text{cm}}^2}}$

 

$\text{IV wiersz tabeli}$  

$P_p=\frac{a^2\sqrt{3}}{4}=\frac{{\left(1\text{cm}\right)}^2\cdot \sqrt{3}}{4}=\underline{\underline{\frac{\sqrt{3}}{4}{\text{cm}}^2}}$  

$P_b=3\cdot \frac{1}{2}\cdot 1\text{cm}\cdot 2\text{cm}=\underline{\underline{3{\text{cm}}^2}}$  

$P_c=\frac{\sqrt{3}}{4}\text{cm}+3{\text{cm}}^2=\underline{\underline{\left(\frac{\sqrt{3}}{4}+3\right){\text{cm}}^2}}$  

 

$\text{V wiersz tabeli}$   

$P_p=9\sqrt{3}{\text{cm}}^2$  

$\frac{a^2\sqrt{3}}{4}=9\sqrt{3}{\text{cm}}^2\mid \cdot 4$  

$a^2\sqrt{3}=36\sqrt{3}{\text{cm}}^2\mid :\sqrt{3}$  

$a^2=36{\text{cm}}^2\mid \sqrt{}$  

$a=\sqrt{36}\text{cm}=\underline{\underline{6\text{cm}}}$  

$P_b=3\cdot \frac{1}{{\sout{2}}^1}\cdot {\sout{6}}^3\text{cm}\cdot 6\text{cm}=\underline{\underline{54{\text{cm}}^2}}$  

$P_c=9\sqrt{3}{\text{cm}}^2+54{\text{cm}}^2=\underline{\underline{\left(9\sqrt{3}+54\right){\text{cm}}^2}}$  

 

$\text{VI wiersz tabeli}$  

$P_p=\frac{{\left(2\text{cm}\right)}^2\cdot \sqrt{3}}{4}=\frac{4\cdot \sqrt{3}}{4}{\text{cm}}^2=\underline{\underline{\sqrt{3}{\text{cm}}^2}}$  

$P_c=P_p+P_b$  

$4\sqrt{3}{\text{cm}}^2=\sqrt{3}{\text{cm}}^2+P_b\mid -\sqrt{3}{\text{cm}}^2$  

$P_b=\underline{\underline{3\sqrt{3}{\text{cm}}^2}}$  

$3\cdot \frac{1}{2}\cdot 2\text{cm}\cdot h=3\sqrt{3}{\text{cm}}^2$  

$3\text{cm}\cdot h=3\sqrt{3}{\text{cm}}^2\mid :3\text{cm}$  

$h=\underline{\underline{\sqrt{3}\text{cm}}}$  

 

$\text{VII wiersz tabeli}$  

$P_p=6\cdot \frac{{\left(3\text{cm}\right)}^2\cdot \sqrt{3}}{4}={\sout{6}}^3\cdot \frac{9{\text{cm}}^2\cdot \sqrt{3}}{{\sout{4}}^2}=3\cdot \frac{9\sqrt{3}{\text{cm}}^2}{2}=\frac{27\sqrt{3}{\text{cm}}^2}{2}=\underline{\underline{13\frac{1}{3}\sqrt{3}{\text{cm}}^2}}$  

$P_b={\sout{6}}^3\cdot \frac{1}{{\sout{2}}^1}\cdot 3\text{cm}\cdot 5\text{cm}=\underline{\underline{45{\text{cm}}^2}}$  

$P_c=13\frac{1}{3}\sqrt{3}{\text{cm}}^2+45{\text{cm}}^2=\underline{\underline{\left(13\frac{1}{3}\sqrt{3}+45\right){\text{cm}}^2}}$     

 

$\text{VIII wiersz tabeli}$  

$P_p={\sout{6}}^3\cdot \frac{a^2\sqrt{3}}{{\sout{4}}^2}=\frac{3a^2\sqrt{3}}{2}$   

$6\sqrt{3}{\text{cm}}^2=\frac{3a^2\sqrt{3}}{2}\mid :3$  

$2\sqrt{3}{\text{cm}}^2=\frac{a^2\sqrt{3}}{2}\mid \cdot 2$  

$4\sqrt{3}{\text{cm}}^2=a^2\sqrt{3}\mid :\sqrt{3}$  

$a^2=4{\text{cm}}^2\mid \sqrt{}$  

$a=\underline{\underline{2\text{cm}}}$  

$P_b={\sout{6}}^3\cdot \frac{1}{{\sout{2}}^1}\cdot 2\text{cm}\cdot 7\text{cm}=\underline{\underline{42{\text{cm}}^2}}$  

$P_c=6\sqrt{3}{\text{cm}}^2+42{\text{cm}}^2=\underline{\underline{\left(6\sqrt{3}+42\right){\text{cm}}^2}}$   

 

$\text{IX wiersz tabeli}$    

$P_p={\sout{6}}^3\cdot \frac{{\left(2\text{cm}\right)}^2\cdot \sqrt{3}}{{\sout{4}}^2}=3\cdot \frac{4\sqrt{3}{\text{cm}}^3}{2}=3\cdot 2\sqrt{3}{\text{cm}}^2=\underline{\underline{6\sqrt{3}{\text{cm}}^2}}$  

$P_b=60{\text{cm}}^2$  

$P_b={\sout{6}}^3\cdot \frac{1}{{\sout{2}}^1}\cdot a\cdot h$  

$60{\text{cm}}^2=3\cdot 2\text{cm}\cdot h$  

$60{\text{cm}}^2=6\text{cm}\cdot h\mid :6\text{cm}$  

$h=\underline{\underline{10\text{cm}}}$  

 

$P_c=6\sqrt{3}{\text{cm}}^2+60{\text{cm}}^2=\underline{\underline{\left(6\sqrt{3}+60\right){\text{cm}}^2}}$