Polygons

9000045706

Level: 
B
Given a regular pentagon with the side \(a\), find the radius \(r\) of the circle circumscribed to this pentagon.
\(r = \frac{a} {2\cdot \cos 54^{\circ }}\)
\(r = \frac{2a} {\cos 72^{\circ }}\)
\(r = \frac{2a} {\cos 54^{\circ }}\)
\(r = \frac{a} {2\cdot \cos 72^{\circ }}\)

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.
\(20\, \mathrm{cm}\)
\(18\, \mathrm{cm}\)
\(19\, \mathrm{cm}\)
\(21\, \mathrm{cm}\)

9000020910

Level: 
A
The perimeter of a rectangle is \(28\, \mathrm{cm}\). The diagonal of this rectangle is \(10\, \mathrm{cm}\). Find the sides of the rectangle.
\(8\, \mathrm{cm}\) and \(6\, \mathrm{cm}\)
\(7\, \mathrm{cm}\) and \(7\, \mathrm{cm}\)
\(9\, \mathrm{cm}\) and \(5\, \mathrm{cm}\)
\(7\, \mathrm{cm}\) and \(3\, \mathrm{cm}\)