Polygons

1103054911

Level: 
B
The lengths of sides of the parallelogram \( ABCD \) are \( 8\,\mathrm{cm} \) and \( 6\,\mathrm{cm} \). The size of one of its interior angles is \( 60^{\circ} \). Calculate the area of the parallelogram.
\( 24\sqrt3\,\mathrm{cm}^2 \)
\( 12\sqrt3\,\mathrm{cm}^2 \)
\( 24\,\mathrm{cm}^2 \)
\( 12\,\mathrm{cm}^2 \)

1103054910

Level: 
C
In the kite \( ABCD \), \( |AB| = |BC| = 12\,\mathrm{cm} \), \( |CD| = |DA| = 6\,\mathrm{cm} \), and the measure of \( \measuredangle DAB \) is \( 120^{\circ} \). Calculate the area of the kite.
\( 36\sqrt3\,\mathrm{cm}^2 \)
\( 24\sqrt3\,\mathrm{cm}^2 \)
\( 18\sqrt3\,\mathrm{cm}^2 \)
\( 36\,\mathrm{cm}^2 \)

1103054909

Level: 
B
In the convex quadrilateral \( ABCD \), \( |AB| = |DA| = 20\,\mathrm{cm} \), \( |BC| = |CD| = 15\,\mathrm{cm} \). The diagonal \( AC \) is \( 25\,\mathrm{cm} \) long. Give the measure of the angle \( ABC \).
\( 90^{\circ} \)
\( 37^{\circ} \)
\( 53^{\circ} \)
\( 72^{\circ} \)

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.
\( 100^{\circ} \)
\( 160^{\circ} \)
\( 200^{\circ} \)
\( 120^{\circ} \)

1103054907

Level: 
C
The picture shows a kite. Give the measures of all interior angles \( \alpha \), \( \beta \), \( \gamma \) and \( \delta \).
\( \alpha = 124^{\circ} \), \( \beta = 108^{\circ} \), \( \gamma = 20^{\circ} \), \( \delta = 108^{\circ} \)
\( \alpha = 124^{\circ} \), \( \beta = 108^{\circ} \), \( \gamma = 124^{\circ} \), \( \delta = 108^{\circ} \)
\( \alpha = 124^{\circ} \), \( \beta = 72^{\circ} \), \( \gamma = 20^{\circ} \), \( \delta = 72^{\circ} \)
\( \alpha = 124^{\circ} \), \( \beta = 108^{\circ} \), \( \gamma = 72^{\circ} \), \( \delta = 83^{\circ} \)

1103054906

Level: 
B
\( ABCD \) is a trapezium with bases \( |AB| = 8\,\mathrm{cm} \) and \( |CD| = 4\,\mathrm{cm} \). Calculate the area of the triangle \( ABS \) if the area of the triangle \( CDS \) is \( 12\,\mathrm{cm}^2 \), where \( S \) is the intersection point of the diagonals \( BD \) and \( AC \).
\( 48\,\mathrm{cm}^2 \)
\( 24\,\mathrm{cm}^2 \)
\( 6\,\mathrm{cm}^2 \)
\( 3\,\mathrm{cm}^2 \)

1103054902

Level: 
B
Let \( ABCD \) be a trapezium with the base $AB$ of \( 8\,\mathrm{cm} \). The remaining sides have the same length. The measure of \( \measuredangle DAB \) is \( 60^{\circ} \). Calculate the perimeter of the trapezium.
\( 20\,\mathrm{cm} \)
\( 4\,\mathrm{cm} \)
\( 14\,\mathrm{cm} \)
\( 24\,\mathrm{cm} \)