9000121804
Level:
B
Find the number of vertices of a regular polygon with
\(27\)
diagonals.
\(9\)
\(18\)
\(6\)
\(24\)
Polygons
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.
\(108\)
\(144\)
\(112\)
\(72\)
9000121806
Level:
B
The measure of the interior angle in a regular polygon is \(160^{\circ}\). Find the number of vertices of this polygon. In the figure the interior angle (marked in red) of a regular hexagon is shown.
\(18\)
\(16\)
\(32\)
\(9\)
9000121808
Level:
B
The number of diagonals in a polygon is three times bigger than the number of sides
of this polygon. Find the number of vertices of this polygon.
\(9\)
\(12\)
\(6\)
\(15\)
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.
\(\rho = \frac{a}
{2\cdot \mathop{\mathrm{tg}}\nolimits 30^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 30^{\circ }\)
\(\rho = \frac{2a}
{\mathop{\mathrm{tg}}\nolimits 30^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 60^{\circ }\)