Polygons
2010018004
Level:
C
A rectangle-shaped land has dimensions \(5 \times 8\,\mathrm{cm}\) on a map with scale \(1:500\). The owner increased the size of his land by buying some land from his neighbor. The new land has dimensions \(7\times 9\,\mathrm{cm}\) on the map. Find the actual increase of the perimeter of the land (i.e. find the increase in the length of the fence required to enclose the whole land). Give your answer in meters.
\(30\,\mathrm{m}\)
\(15\,\mathrm{m}\)
\(40\,\mathrm{m}\)
\(60\,\mathrm{m}\)
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.
\(13\)
\(15\)
\(10\)
\(12\)
2010018002
Level:
B
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, the blue angle is the interior angle of the polygon. Suppose we consider a regular polygon with the central angle of \(30^{\circ}\), then find the measure of the interior angle of this polygon.
\(150^{\circ}\)
\(180^{\circ}\)
\(90^{\circ}\)
\(210^{\circ}\)
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.
\(12\)
\(15\)
\(18\)
\(8\)
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.
\(135^{\circ}\)
\(120^{\circ}\)
\(150^{\circ}\)
\(45^{\circ}\)
2010015007
Level:
B
Find the number of diagonals in the regular octagon (a regular polygon with
\(8\)
vertices).
\(20\)
\( 24 \)
\( 8 \)
\( 40\)
2010015009
Level:
B
Find the number of vertices of a regular polygon with
\(14\)
diagonals.
\(7\)
\( 14 \)
\( 9 \)
\( 12 \)
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.
\(24\)
\( 12 \)
\( 20 \)
\( 18 \)
2010015006
Level:
B
The figure shows a rectangular trapezium whose bases have lengths of \( 19\,\mathrm{cm} \) and \( 14\,\mathrm{cm} \), and the longer arm is \( 13\,\mathrm{cm} \) long. Calculate the sine of angle \(\alpha\).
\( \frac{12}{13} \)
\( \frac{5}{13} \)
\( 22.62^{\circ} \)
\( 67.38^{\circ} \)