2010015007
Level:
B
Find the number of diagonals in the regular octagon (a regular polygon with
\(8\)
vertices).
\(20\)
\( 24 \)
\( 8 \)
\( 40\)
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.
\(24\)
\( 12 \)
\( 20 \)
\( 18 \)
2010015009
Level:
B
Find the number of vertices of a regular polygon with
\(14\)
diagonals.
\(7\)
\( 14 \)
\( 9 \)
\( 12 \)
2010015010
Level:
B
For a regular octagon find the interior angle. In the figure a regular octagon with an interior angle marked in red is shown.
\(135^{\circ}\)
\(120^{\circ}\)
\(150^{\circ}\)
\(45^{\circ}\)
2010018001
Level:
B
The measure of the interior angle in a regular polygon is \(150^{\circ}\). Find the number of vertices of this polygon. In the figure the interior angle (marked in red) of a regular hexagon is shown.
\(12\)
\(15\)
\(18\)
\(8\)
2010018003
Level:
B
The number of diagonals in a polygon is five times bigger than the number of sides of this polygon. Find the number of vertices of this polygon.
\(13\)
\(15\)
\(10\)
\(12\)
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.
\(20\, \mathrm{cm}\)
\(18\, \mathrm{cm}\)
\(19\, \mathrm{cm}\)
\(21\, \mathrm{cm}\)
9000045706
Level:
B
Given a regular pentagon with the side
\(a\), find the
radius \(r\) of
the circle circumscribed to this pentagon.
\(r = \frac{a}
{2\cdot \cos 54^{\circ }}\)
\(r = \frac{2a}
{\cos 72^{\circ }}\)
\(r = \frac{2a}
{\cos 54^{\circ }}\)
\(r = \frac{a}
{2\cdot \cos 72^{\circ }}\)
9000045707
Level:
B
Given a regular pentagon with the side
\(a\), find the
radius \(\rho \) of
the circle inscribed to this pentagon.
\(\rho = \frac{a}
{2} \cdot \mathop{\mathrm{tg}}\nolimits 54^{\circ }\)
\(\rho = \frac{2a}
{\mathop{\mathrm{tg}}\nolimits 54^{\circ }}\)
\(\rho = \frac{a}
{2\cdot \mathop{\mathrm{tg}}\nolimits 54^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 54^{\circ }\)