Polygons

1103021303

Level: 
A
A rectangle with sides \( a \), \( b \) is given. The angle between diagonals \( \alpha = 60^{\circ} \). The longer side \( a = 6\,\mathrm{cm} \). Calculate the length of the shorter side \( b \).
\( \frac6{\sqrt3}\,\mathrm{cm} \)
\( \frac3{\sqrt3}\,\mathrm{cm} \)
\( \frac1{\sqrt3}\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)

9000150502

Level: 
C
Two hotels and a lake are in a satellite photo. The distance between the hotels is \(400\, \mathrm{m}\) which is \(4\, \mathrm{cm}\) in the photo. The area of the lake in the photo is \(30\, \mathrm{cm}^{2}\). Find the real area of the lake.
\(3\cdot 10^{5}\, \mathrm{m}^{2}\)
\(3\cdot 10^{1}\, \mathrm{m}^{2}\)
\(3\cdot 10^{3}\, \mathrm{m}^{2}\)
There is not enough information to solve this problem.

9000121809

Level: 
B
The number of diagonals in a regular polygon is \(2.5\)-times bigger than the number of the sides of this polygon. In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find the central angle of the polygon.
\(45^{\circ }\)
\(50^{\circ }\)
\(135^{\circ }\)
\(35^{\circ }\)

9000121802

Level: 
B
Consider a regular polygon with the central angle of \(20^{\circ }\). In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find the number of vertices of this polygon.
\(18\)
\(9\)
\(20\)
\(15\)