Polygons

1103021407

Level: 
B
The vertical cross-section of the embankment around the pond has the shape of an isosceles trapezium. Calculate the angle of inclination of the embankment if the embankment is \( 2\,\mathrm{m} \) high, the top width is \( 3\,\mathrm{m} \) and the arms are \( 4\,\mathrm{m} \) long.
\( 30^{\circ} \)
\( 60^{\circ} \)
\( 26.57^{\circ} \)
\( 45^{\circ} \)

1103021405

Level: 
A
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.
\( 53.13^{\circ} \)
\( 38.94^{\circ} \)
\( 36.87^{\circ} \)
\( 106.26^{\circ} \)

1103021403

Level: 
A
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: 
A
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: 
C
\( ABCD \) 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: 
B
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.