Project ID:
5000000052
Accepted:
Template:
Question:
The base $ABCD$ of a square pyramid $ABCDV$ has an edge of $6\,\mathrm{cm}$. The height of the pyramid is $8\,\mathrm{cm}$. Let $S$ be the midpoint of the base, $P$ the midpoint of the edge $AV$, and $Q$ the midpoint of the edge $CV$ (see the picture). Find the distance between
Question Row 1:
\ifen the point $A$ and the point $S$ \fi \ifcs bodem $A$ a bodem $S$ \fi \ifpl punktem $A$ i punktem $S$ \fi \ifsk bodom $A$ bodom $S$ \fi \ifes el punto $A$ y el punto $S$ \fi
Answer Row 1:
$\frac32\sqrt2\,\mathrm{cm}$, $4\,\mathrm{cm}$, *$3\sqrt2\,\mathrm{cm}$, $\sqrt{82}\,\mathrm{cm}$
Question Row 2:
\ifen the point $P$ and the point $Q$ \fi \ifcs bodem $P$ a bodem $Q$ \fi \ifpl punktem $P$ i punktem $Q$ \fi \ifsk bodom $P$ bodom $Q$ \fi \ifes el punto $P$ y el punto $Q$ \fi
Answer Row 2:
*$3\sqrt2\,\mathrm{cm}$, $8\,\mathrm{cm}$, $\sqrt{34}\,\mathrm{cm}$, $\sqrt{73}\,\mathrm{cm}$
Question Row 3:
\ifen the point $V$ and the point $A$ \fi \ifcs bodem $V$ a bodem $A$ \fi \ifpl punktem $V$ i punktem $A$ \fi \ifsk bodom $V$ bodom $A$ \fi \ifes el punto $V$ y el punto $A$ \fi
Answer Row 3:
$\frac32\sqrt2\,\mathrm{cm}$, $4\,\mathrm{cm}$, $3\sqrt2\,\mathrm{cm}$, *$\sqrt{82}\,\mathrm{cm}$
Question Row 4:
\ifen the point $P$ and the line $VS$ \fi \ifcs bodem $P$ a přímkou $VS$ \fi \ifpl punktem $P$ i prostą $VS$ \fi \ifsk bodom $P$ a priamkou $VS$ \fi \ifes el punto $P$ y la recta $VS$ \fi
Answer Row 4:
*$\frac32\sqrt2\,\mathrm{cm}$, $8\,\mathrm{cm}$, $\sqrt{73}\,\mathrm{cm}$, $\sqrt{82}\,\mathrm{cm}$
Question Row 5:
\ifen the point $V$ and the line $BC$ \fi \ifcs bodem $V$ a přímkou $BC$ \fi \ifpl punktem $V$ i prostą $BC$ \fi \ifsk bodom $V$ a priamkou $BC$ \fi \ifes el punto $V$ y la recta $BC$ \fi
Answer Row 5:
$3\sqrt2\,\mathrm{cm}$, $4\,\mathrm{cm}$, *$\sqrt{73}\,\mathrm{cm}$, $\sqrt{82}\,\mathrm{cm}$
Question Row 6:
\ifen the point $B$ and the line $PQ$ \fi \ifcs bodem $B$ a přímkou $PQ$ \fi \ifpl punktem $B$ i prostą $PQ$ \fi \ifsk bodom $B$ a priamkou $PQ$ \fi \ifes el punto $B$ y la recta $PQ$ \fi
Answer Row 6:
$5\,\mathrm{cm}$, *$\sqrt{34}\,\mathrm{cm}$, $\sqrt{73}\,\mathrm{cm}$, $\sqrt{82}\,\mathrm{cm}$
Question Row 7:
\ifen the line $AC$ and the line $PQ$ \fi \ifcs přímkou $AC$ a přímkou $PQ$ \fi \ifpl prostą $AC$ i prostą $PQ$ \fi \ifsk bodom $AC$ a priamkou $PQ$ \fi \ifes la recta $AC$ y la recta $PQ$ \fi
Answer Row 7:
$\frac32\sqrt3\,\mathrm{cm}$, *$4\,\mathrm{cm}$, $3\sqrt2\,\mathrm{cm}$, $6\,\mathrm{cm}$
Question Row 8:
\ifen the point $Q$ and the plane $ABC$ \fi \ifcs bodem $Q$ a rovinou $ABC$ \fi \ifpl punktem $Q$ i płaszczyzną $ABC$ \fi \ifsk bodom $Q$ a rovinou $ABC$ \fi \ifes el punto $Q$ y el plano $ABC$ \fi
Answer Row 8:
$\frac32\sqrt2\,\mathrm{cm}$, *$4\,\mathrm{cm}$, $6\,\mathrm{cm}$, $8\,\mathrm{cm}$
Tex:
% tiket 33346
\let\oldQuestion\Question
\def\Question{
\begin{minipage}[t]{0.6\linewidth}
\leavevmode
\oldQuestion
\end{minipage}
\hfill
\begin{minipage}[t]{0.35\linewidth}
\leavevmode
\kern -30pt
\obrMsr[x=1.5cm,y=1.5cm,z=0.3cm]{-1}2{-1}2
{
\footnotesize
\pgfmathsetmacro{\cubex}{1}
\pgfmathsetmacro{\cubey}{1}
\pgfmathsetmacro{\cubez}{2}
\coordinate (A) at (0,0,0);
\coordinate (B) at (\cubex,0,0);
\coordinate (C) at (\cubex.2,0,\cubez);
\coordinate (D) at (0.2,0,\cubez);
\coordinate (V) at (0.6,1.5,1);
\coordinate (P) at ($(A)!0.5!(V)$);
\coordinate (Q) at ($(C)!0.5!(V)$);
\draw[thick,dashed] (A) -- (D) node [yshift=4pt,xshift=-6pt]{$D$} -- (C) node [yshift=-5pt,xshift=5pt]{$C$};
\draw[dashed] (A) -- (C);
\draw[dashed] (B) -- (D);
\draw (0.6,0,1) node [below,xshift=-2pt,yshift=1pt]{$S$};
\draw[thick] (A) node [yshift=-5pt,xshift=-5pt]{$A$} -- (B) node [yshift=-6pt,xshift=3pt]{$B$} --(C);
\draw[thick] (A) -- (V) node [above]{$V$};
\draw[thick] (B) -- (V);
\draw[thick] (C) -- (V);
\draw[thick,dashed] (D) -- (V);
\draw[dashed] (0.6,0,1) -- (V);
\begin{scope}[thick]
\obrKrizek[2pt]{P}{above left}{P}
\obrKrizek[2pt]{Q}{above right}{Q}
\end{scope}
}
\end{minipage}
\kern -20pt}
\MsrTabulka[0pt]{0.4\linewidth}{0.6\linewidth}
\pocetsloupcu{4}