1103054903
Level:
B
The picture shows a rectangular trapezium. Give the sum of its largest interior angle and the smallest interior angle.
\( 180^{\circ} \)
\( 90^{\circ} \)
\( 175^{\circ} \)
\( 150^{\circ} \)
Polygons
1103054904
Level:
B
The profile of a trench has the shape of an isosceles trapezium, as shown in the picture. Determine the width of the trench.
\( 7\,\mathrm{m} \)
\( 5\,\mathrm{m} \)
\( 2\,\mathrm{m} \)
\( 4\,\mathrm{m} \)
1103054905
Level:
B
In the isosceles trapezium \( ABCD \), \( |AD|=|BC| \), \( |AB|=|AC| \) and the measure of the angle \( BAC \) is \( 40^{\circ} \). What is the measure of the angle \( ADC \)?
\( 110^{\circ} \)
\( 120^{\circ} \)
\( 100^{\circ} \)
\( 130^{\circ} \)
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 \( AC \).
\( 48\,\mathrm{cm}^2 \)
\( 24\,\mathrm{cm}^2 \)
\( 6\,\mathrm{cm}^2 \)
\( 3\,\mathrm{cm}^2 \)
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.
\( 5.6\,\mathrm{cm} \)
\( 5.1\,\mathrm{cm} \)
\( 4.8\,\mathrm{cm} \)
\( 6.2\,\mathrm{cm} \)
1103055004
Level:
B
A regular pentagon is inscribed in a circle of radius \( 10\,\mathrm{cm} \). Calculate the perimeter of the pentagon. Round the result to two decimal places.
\( 58.78\,\mathrm{cm} \)
\( 5.88\,\mathrm{cm} \)
\( 11.76\,\mathrm{cm} \)
\( 80.90\,\mathrm{cm} \)
1103055008
Level:
B
\( ABCDEF \) is a regular hexagon. (See the picture.) The area of the triangle \( ABC \) is \( 6\,\mathrm{cm}^2 \). Calculate the area of the hexagon.
\( 36\,\mathrm{cm}^2 \)
\( 24\,\mathrm{cm}^2 \)
\( 30\,\mathrm{cm}^2 \)
\( 42\,\mathrm{cm}^2 \)
1103055009
Level:
B
The regular hexagon \( ABCDEF \) is in the picture. The area of the triangle \( ABC \) is \( 10\,\mathrm{cm}^2 \). Calculate the length of the side of the hexagon. Round to one decimal place.
\( 4.8\,\mathrm{cm} \)
\( 23.1\,\mathrm{cm} \)
\( 6.3\,\mathrm{cm} \)
\( 7.2\,\mathrm{cm} \)