Polygons

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

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 \( ABC \).
\( 90^{\circ} \)
\( 37^{\circ} \)
\( 53^{\circ} \)
\( 72^{\circ} \)

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.
\( 24\sqrt3\,\mathrm{cm}^2 \)
\( 12\sqrt3\,\mathrm{cm}^2 \)
\( 24\,\mathrm{cm}^2 \)
\( 12\,\mathrm{cm}^2 \)

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.
\( 12\,\mathrm{cm}^2 \)
\( 24\,\mathrm{cm}^2 \)
\( 4\sqrt3\,\mathrm{cm}^2 \)
\( 6\,\mathrm{cm}^2 \)

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.
\( 5.6\,\mathrm{cm} \)
\( 5.1\,\mathrm{cm} \)
\( 4.8\,\mathrm{cm} \)
\( 6.2\,\mathrm{cm} \)

1103055001

Level: 
B
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?
\( 96\,\mathrm{m}^2 \)
\( 48\,\mathrm{m}^2 \)
\( 124\,\mathrm{m}^2 \)
\( 140\,\mathrm{m}^2 \)