2010015007
Level:
B
Find the number of diagonals in the regular octagon (a regular polygon with
\(8\)
vertices).
\(20\)
\( 24 \)
\( 8 \)
\( 40\)
Polygons
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.
\(24\)
\( 12 \)
\( 20 \)
\( 18 \)
2010015005
Level:
B
Given the isosceles trapezium \( ABCD \), where \( |AB| = 12\,\mathrm{cm} \), \( |BC| = 4\,\mathrm{cm} \), \( |CD| = 16\,\mathrm{cm} \), and \( |AD| = 4\,\mathrm{cm} \), determine the measure of \( \measuredangle BCD \).
\( 60^{\circ} \)
\( 70^{\circ} \)
\( 45^{\circ} \)
\( 120^{\circ} \)
2010015004
Level:
B
The isosceles trapezium \( ABCD \) is in the picture. The measure of the angle \( DAB \) is \( 60^{\circ} \). Determine the measure of the angle \( BCD \).
\( 120^{\circ} \)
\( 60^{\circ} \)
\( 110^{\circ} \)
\( 150^{\circ} \)
2010015003
Level:
C
\( ABCD \) is a rhombus, the measure of the angle \( DAB \) is \(70^{\circ}\) and the shorter diagonal \( u = 50\,\mathrm{cm} \). Determine the height \(v\) of the rhombus. Round the result to two decimal places.
\( 40.96\,\mathrm{cm} \)
\( 28.68\,\mathrm{cm} \)
\( 71.41\,\mathrm{cm} \)
\( 46.98\,\mathrm{cm} \)
2010015001
Level:
A
The side lengths of the rectangle \( ABCD \) are in the ratio \( AB: BC=4:3 \). Give the degree measure of the angle \( ASB \). Round the result to two decimal places.
\( 106.26^{\circ} \)
\( 73.74^{\circ} \)
\( 104.26^{\circ} \)
\( 75.74^{\circ} \)
2010012901
Level:
C
Consider a circle \( k \) with radius \( 5\,\mathrm{cm} \). In the circle is inscribed a convex quadrilateral \( ABCD \) so that the diagonal \( AC \) is the diameter of the circle, the length of \( BC \) is \( 8\,\mathrm{cm} \), and the length of \( DC \) is \( 5\,\mathrm{cm} \). Determine the length of side \( AD \). (See the picture.)
\(5 \sqrt{3}\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)
\( 10\,\mathrm{cm} \)
\(3 \sqrt{5}\,\mathrm{cm} \)
2010012809
Level:
B
Which of the following formulas expresses the area of a regular pentagon inscribed in a circle of radius \( r \)? (See the picture.)
\( \frac{5r^2\sin72^{\circ}}2\)
\( \frac{10r^2\sin72^{\circ}}2\)
\( \frac{5r^2\sin36^{\circ}}2\)
\( \frac{5r \sin36^{\circ}}2\)
2010011205
Level:
A
A diagonal of a rectangle has length of \( 26\,\mathrm{cm} \) and the perimeter of the rectangle is \( 68\,\mathrm{cm} \). Find the difference of the length and the width of the rectangle in centimeters.
\( 14 \)
\( 20 \)
\( 24 \)
\( 28\)