Polygons

1103055001

Level: 
C
The picture shows an intersection of two streets. Two water carts passed the intersection while sprinkling entire surface of the street. Each of the carts continued along the street it came. Determine how many square meters of the streets surface were sprinkled twice?
\( 96\,\mathrm{m}^2 \)
\( 48\,\mathrm{m}^2 \)
\( 124\,\mathrm{m}^2 \)
\( 140\,\mathrm{m}^2 \)

1103054913

Level: 
B
The area of the parallelogram \( ABCD \) is \( 12\,\mathrm{cm}^2 \), the lengths of its sides are \( 8\,\mathrm{cm} \) and \( 3\,\mathrm{cm} \), as shown in the diagram. Calculate the length of the shorter diagonal. Round the result to one decimal place.
\( 5.6\,\mathrm{cm} \)
\( 5.1\,\mathrm{cm} \)
\( 4.8\,\mathrm{cm} \)
\( 6.2\,\mathrm{cm} \)

1103054912

Level: 
B
Let \( ABCD \) be a parallelogram with \( |AB| = 8\,\mathrm{cm} \), \( |BC| = 3\,\mathrm{cm} \) and the measure of \( \measuredangle DAB \) is \( 30^{\circ} \). Give the area of the parallelogram.
\( 12\,\mathrm{cm}^2 \)
\( 24\,\mathrm{cm}^2 \)
\( 4\sqrt3\,\mathrm{cm}^2 \)
\( 6\,\mathrm{cm}^2 \)

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: 
C
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: 
A
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 \( AC \).
\( 48\,\mathrm{cm}^2 \)
\( 24\,\mathrm{cm}^2 \)
\( 6\,\mathrm{cm}^2 \)
\( 3\,\mathrm{cm}^2 \)