1003021404
Level:
B
A rhombus has a side \( 4\,\mathrm{cm} \) long. Give the measure of the angle between the diagonals.
\( 90^{\circ} \)
\( 60^{\circ} \)
\( 30^{\circ} \)
\( 20^{\circ} \)
Polygons
1003054908
Level:
B
A quadrilateral is symmetric across one of its diagonals and can be inscribed in a circle. The measure of one of its interior angles is \( 80^{\circ} \). Determine the measure of its largest interior angle.
\( 100^{\circ} \)
\( 160^{\circ} \)
\( 200^{\circ} \)
\( 120^{\circ} \)
1003055003
Level:
B
How many vertices does a convex polygon have, if the arithmetic mean of its interior angles is \( 140 \)?
\( 9 \)
\( 8 \)
\( 10 \)
\( 12 \)
1003055005
Level:
B
The side of a regular hexagon is \( 4\,\mathrm{cm} \) long. Which of the numbers gives the area of the hexagon?
\( 24\sqrt3\,\mathrm{cm}^2 \)
\( 4\sqrt3\,\mathrm{cm}^2 \)
\( 48\sqrt3\,\mathrm{cm}^2 \)
\( 20\sqrt3\,\mathrm{cm}^2 \)
1003055006
Level:
B
A regular pentadecagon (\( 15 \) sided polygon) is inscribed in a circle of radius \( 8\,\mathrm{cm} \). Calculate its area. Round the result to two decimal places.
\( 195.23\,\mathrm{cm}^2 \)
\( 97.62\,\mathrm{cm}^2 \)
\( 13.02\,\mathrm{cm}^2 \)
\( 24.40\,\mathrm{cm}^2 \)
1003055007
Level:
B
In a regular decagon (\( 10 \) sided polygon) the length of the side is \( 4\,\mathrm{cm} \). Which of the given numbers most accurately expresses fits its area most accurately?
\( 123\,\mathrm{cm}^2 \)
\( 12\,\mathrm{cm}^2 \)
\( 55\,\mathrm{cm}^2 \)
\( 185\,\mathrm{cm}^2 \)
1103021401
Level:
B
\( ABCD \) is a rhombus, the height \( v = 48\,\mathrm{cm} \) and the shorter diagonal \( u = 60\,\mathrm{cm} \). Determine the measure of the acute interior angle of the rhombus. Round the result to two decimal places.
\( 73.74^{\circ} \)
\( 36.87^{\circ} \)
\( 24.12^{\circ} \)
\( 27.13^{\circ} \)
1103021402
Level:
B
The area of a rhombus is \( 200\,\mathrm{cm}^2 \). Give the measure of the acute interior angle of the rhombus if the length of its side is \( 15\,\mathrm{cm} \). Round the result to two decimal places.
\( 62.73^{\circ} \)
\( 27.28^{\circ} \)
\( 41.63^{\circ} \)
\( 12.13^{\circ} \)
1103021403
Level:
B
Given the rhombus \( ABCD \) with the diagonal \( |DB|= 8\,\mathrm{cm} \). The measure of \( \measuredangle DAB \) is \( 60^{\circ} \). Calculate the circumference of the rhombus.
\( 32\,\mathrm{cm} \)
\( 18.48\,\mathrm{cm} \)
\(64\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)
1103021405
Level:
B
A side of a rhombus is \( 35\,\mathrm{cm} \) long and the length of one of its diagonals is \( 56\,\mathrm{cm} \). Give the measure of the angle that the other diagonal makes with the side of the rhombus. Round the result to two decimal places.
\( 53.13^{\circ} \)
\( 38.94^{\circ} \)
\( 36.87^{\circ} \)
\( 106.26^{\circ} \)