Metric properties

1103107014

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the line \( BA’ \) and the plane \( AEE’ \) (see the picture). Round the result to two decimal places.
\( 26.57^{\circ} \)
\( 63.43^{\circ} \)
\( 30^{\circ} \)
\( 22.5^{\circ} \)

1103107013

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the plane \( BCC' \) and the plane \( CDD' \) (see the picture).
\( 60^{\circ} \)
\( 120^{\circ} \)
\( 90^{\circ} \)
\( 72^{\circ} \)

1103107012

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the plane \( ADD' \) and the plane \( CDD' \) (see the picture).
\( 60^{\circ} \)
\( 45^{\circ} \)
\( 90^{\circ} \)
\( 72^{\circ} \)

1103107011

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the line \( FC' \) and the base plane \( ABC \) (see the picture).
\( 45^{\circ} \)
\( 60^{\circ} \)
\( 30^{\circ} \)
\( 72^{\circ} \)

1103107010

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the distance between the points \( E' \) and \( C \) (see the picture).
\( 4\sqrt7\,\mathrm{cm} \)
\( 8\sqrt2\,\mathrm{cm} \)
\( 8+4\sqrt3\,\mathrm{cm} \)
\( 16\sqrt7\,\mathrm{cm} \)

1103107009

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the distance between the points \( F' \) and \( C \) (see the picture).
\( 8\sqrt2\,\mathrm{cm} \)
\( 4\sqrt5\,\mathrm{cm} \)
\( 4\sqrt7\,\mathrm{cm} \)
\( 4\sqrt2\,\mathrm{cm} \)

1103107008

Level: 
C
A regular hexagonal prism \( ABCDEFA'B'C'D'E'F' \) has the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 6\,\mathrm{cm} \). Let \( S \) be the middle of the top face \( A'B'C'D'E'F' \). Find the distance between the point \( S \) and the line \( BC \) (see the picture).
\( 4\sqrt3\,\mathrm{cm} \)
\( 2\sqrt{13}\,\mathrm{cm} \)
\( 2\sqrt{21}\,\mathrm{cm} \)
\( 4\sqrt{21}\,\mathrm{cm} \)