$V_{\text{K}\ddot{\text{o}}\text{rper}}=V_{\text{Quader}}+4\cdot V_{\text{Prisma}}V\_\{\backslash text\{Körper\}\}=V\_\{\backslash text\{Quader\}\}+\; 4\backslash cdot\; V\_\{\backslash text\{Prisma\}\}$

$V_{\text{Quader}}=20\cdot 20\cdot 10=4000V\_\{\backslash text\{Quader\}\}=20\backslash cdot\; 20\backslash cdot\; 10=4000$

$V_{\text{Prisma}}=G_{\text{Prisma}}\cdot h_{\text{Prisma}}V\_\{\backslash text\{Prisma\}\}=G\_\{\backslash text\{Prisma\}\}\backslash cdot\; h\_\{\backslash text\{Prisma\}\}$

$G_{\text{Prisma}}={\displaystyle \frac{1}{2}}\cdot g\cdot h\mathrm{.}G\_\{\backslash text\{Prisma\}\}=\backslash dfrac\{1\}\{2\}\backslash cdot\; g\backslash cdot\; h.$

$g=5cmg=5cm$

Berechne $hh$ mit Hilfe des Satzes des Pythagoras.

$h=\sqrt{{13}^2-5^2}=\sqrt{169-25}=\sqrt{144}=12h=\backslash sqrt\{13^2-5^2\}=\backslash sqrt\{169-25\}=\backslash sqrt\{144\}=12$

$G_{\text{Prisma}}={\displaystyle \frac{1}{2}}\cdot 5\cdot 12=30G\_\{\backslash text\{Prisma\}\}=\backslash dfrac\{1\}\{2\}\backslash cdot\; 5\backslash cdot\; 12=30$

$h_{\text{Prisma}}=10h\_\{\backslash text\{Prisma\}\}=10$

$V_{\text{Prisma}}=30\cdot 10=300V\_\{\backslash text\{Prisma\}\}=30\backslash cdot\; 10=300$

$V_{\text{K}\ddot{\text{o}}\text{rper}}=4000+4\cdot 300=5200V\_\{\backslash text\{Körper\}\}=4000+4\backslash cdot\; 300=5200$