Polygons

2000005504

Level: 
A
Let \(ABCD\) be an arbitrary convex quadrilateral and let’s denote by \(P\), \(Q\), \(R\), \(S\) the centers of the sides \(AB\), \(BC\), \(CD\), \(DA\) in that order. Then, what type of a quadrilateral is \(PQRS\)?
It may or may not be a parallelogram.
It is a rectangle.
It is a rectangle or a square.
It is not a parallelogram.

1103055010

Level: 
B
In the regular hexagon \( ABCDEF \), \( G \) and \( H \) are the midpoints of \( AB \) and \( CD \). What part of the area of the hexagon is covered by the area of the quadrilateral \( BCHG \)? The area of the quadrilateral corresponds to the shaded region in the figure.
\( \frac5{24} \)
\( \frac15 \)
\( \frac1{28} \)
\( \frac5{36} \)

1103055009

Level: 
B
The regular hexagon \( ABCDEF \) is in the picture. The area of the triangle \( ABC \) is \( 10\,\mathrm{cm}^2 \). Calculate the length of the side of the hexagon. Round to one decimal place.
\( 4.8\,\mathrm{cm} \)
\( 23.1\,\mathrm{cm} \)
\( 6.3\,\mathrm{cm} \)
\( 7.2\,\mathrm{cm} \)