Polygons

2010015008

Level: 
B
Consider a regular polygon with the central angle of \(15^{\circ}\). 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.
\(24\)
\( 12 \)
\( 20 \)
\( 18 \)

2010018002

Level: 
B
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, the blue angle is the interior angle of the polygon. Suppose we consider a regular polygon with the central angle of \(30^{\circ}\), then find the measure of the interior angle of this polygon.
\(150^{\circ}\)
\(180^{\circ}\)
\(90^{\circ}\)
\(210^{\circ}\)

9000035005

Level: 
B
The railroad mound has the cross section of a isosceles trapezoid. The lengths of the bases are \(12\, \mathrm{m}\) and \(8\, \mathrm{m}\), the height is \(3\, \mathrm{m}\). Find the angle at the leg and round to the nearest degrees and minutes. See the picture with a isosceles trapezoid.
\(56^{\circ }19'\)
\(41^{\circ }45'\)
\(48^{\circ }11'\)
\(33^{\circ }69'\)

9000035010

Level: 
B
The height of a right trapezoid is \(4\, \mathrm{cm}\). The length of the longer base is \(7\, \mathrm{cm}\) and the angle between this base and the leg of the trapezoid is \(52^{\circ }\). Find the perimeter of the trapezoid and round to the nearest centimeters. See the picture with a right trapezoid.
\(20\, \mathrm{cm}\)
\(18\, \mathrm{cm}\)
\(19\, \mathrm{cm}\)
\(21\, \mathrm{cm}\)

9000046404

Level: 
B
The parallelogram has sides of the length \(5\, \mathrm{cm}\) and \(4\, \mathrm{cm}\) (see the picture). The area of this parallelogram is \(S = 10\sqrt{2}\, \mathrm{cm}^{2}\). Find the measure of the smaller of the interior angles.
\(45^{\circ }\)
\(30^{\circ }\)
\(60^{\circ }\)

9000046406

Level: 
B
Find the area of the regular octagon of the perimeter \(16\, \mathrm{cm}\). Round the result to two decimal places. (The regular octagon is a polygon which has eight sides of equal length, see the picture. The perimeter of the octagon is the sum of the length of all eight sides.)
\(19.31\, \mathrm{cm}^{2}\)
\(3.31\, \mathrm{cm}^{2}\)
\(20.88\, \mathrm{cm}^{2}\)