Polygons

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.)
\(19.31\, \mathrm{cm}^{2}\)
\(3.31\, \mathrm{cm}^{2}\)
\(20.88\, \mathrm{cm}^{2}\)

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 \(3\, \mathrm{cm}\)