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
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.
\( 32\,\mathrm{cm} \)
\( 18.48\,\mathrm{cm} \)
\(64\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)
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.
\( 62.73^{\circ} \)
\( 27.28^{\circ} \)
\( 41.63^{\circ} \)
\( 12.13^{\circ} \)
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.
\( 73.74^{\circ} \)
\( 36.87^{\circ} \)
\( 24.12^{\circ} \)
\( 27.13^{\circ} \)
1003021308
Level:
A
Choose the wrong claim:
The sum of the opposite angles in a rectangle is \( 360^{\circ} \).
The sum of the interior angles of a convex n-gon is \( (n-2)\cdot180^{\circ} \).
If there is just one pair of sides parallel in a quadrilateral and the other side is perpendicular to them, then the quadrilateral is a right-angled trapezium.
At least one of the interior angles in a trapezium is obtuse.
1003021307
Level:
A
Choose the wrong claim:
The diagonals of a rhombus contain an acute angle.
In each parallelogram the opposite angles are congruent.
If one of the interior angles of a quadrilateral is greater than straight angle, the quadrilateral is not convex.
All interior angles in a square are right.
1103021306
Level:
A
In the square \( ABCD \), \( |AB| = 6\,\mathrm{cm} \). Calculate the area of the marked triangle if \( E \) is the midpoint of the side \( AB \).
\( 3\,\mathrm{cm}^2 \)
\( 6\,\mathrm{cm}^2 \)
\( 9\,\mathrm{cm}^2 \)
\( 12\,\mathrm{cm}^2 \)
1103021305
Level:
A
\( ABCD \) is a square. Determine the degree measure of the angle \( EGD \) if the measure of the angle \( CFG \) is \( 50^{\circ} \).
\( 5^{\circ}\)
\( 10^{\circ}\)
\( 15^{\circ}\)
\( 20^{\circ}\)
1103021304
Level:
A
The side lengths of the rectangle \( ABCD \) are in the ratio \( AB:BC=12:5 \). Give the degree measure of the angle \( CAB \). Round the result to two decimal places.
\( 22.62^{\circ} \)
\( 67.38^{\circ} \)
\( 24.62^{\circ} \)
\( 65.38^{\circ} \)
1103021303
Level:
A
A rectangle with sides \( a \), \( b \) is given. The angle between diagonals \( \alpha = 60^{\circ} \). The longer side \( a = 6\,\mathrm{cm} \). Calculate the length of the shorter side \( b \).
\( \frac6{\sqrt3}\,\mathrm{cm} \)
\( \frac3{\sqrt3}\,\mathrm{cm} \)
\( \frac1{\sqrt3}\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)