9000121810
Level:
B
The number of sides of the polygon is
\(4.5\)-times
smaller than the number of the diagonals in this polygon. Find the interior angle of
the polygon.
\(150^{\circ }\)
\(75^{\circ }\)
\(120^{\circ }\)
\(132^{\circ }\)
Polygons
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.
\(18\)
\(9\)
\(20\)
\(15\)
9000121804
Level:
B
Find the number of vertices of a regular polygon with
\(27\)
diagonals.
\(9\)
\(18\)
\(6\)
\(24\)
9000121801
Level:
B
Find the number of diagonals in the regular decagon (a regular polygon with
\(10\)
vertices).
\(35\)
\(7\)
\(10\)
\(70\)
9000121805
Level:
B
For a regular pentagon find the interior angle. In the figure a regular pentagon with an interior angle marked in red is shown.
\(108\)
\(144\)
\(112\)
\(72\)
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.)
\(19.31\, \mathrm{cm}^{2}\)
\(3.31\, \mathrm{cm}^{2}\)
\(20.88\, \mathrm{cm}^{2}\)
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.
\(\rho = \frac{a}
{2} \cdot \mathop{\mathrm{tg}}\nolimits 54^{\circ }\)
\(\rho = \frac{2a}
{\mathop{\mathrm{tg}}\nolimits 54^{\circ }}\)
\(\rho = \frac{a}
{2\cdot \mathop{\mathrm{tg}}\nolimits 54^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 54^{\circ }\)
9000045708
Level:
B
Given a regular hexagon with the side
\(a\), find the
radius \(\rho \) of
the circle inscribed to this hexagon.
\(\rho = \frac{a}
{2\cdot \mathop{\mathrm{tg}}\nolimits 30^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 30^{\circ }\)
\(\rho = \frac{2a}
{\mathop{\mathrm{tg}}\nolimits 30^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 60^{\circ }\)