Polygons

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.
\( 20\,\mathrm{cm} \)
\( 4\,\mathrm{cm} \)
\( 14\,\mathrm{cm} \)
\( 24\,\mathrm{cm} \)

1103054901

Level: 
B
In an isosceles trapezium \( ABCD \) let \( |AB| = 11\,\mathrm{cm} \), \( |BC| = |AD| = 6\,\mathrm{cm} \) and the measure of the angle \( CDA \) be \( 120^{\circ} \). Calculate the length of the side \( CD \).
\( 5\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)
\( 3\,\mathrm{cm} \)
\( 7\,\mathrm{cm} \)

1103021413

Level: 
B
The area of a rectangular trapezium is \( 35\,\mathrm{cm}^2 \). The bases have lengths of \( 6\,\mathrm{cm} \) and \( 8\,\mathrm{cm} \). Express the measure of the angle between the longer base and the longer arm of the trapezium. Round the result to one decimal place.
\( 68.2^{\circ} \)
\( 23.6^{\circ} \)
\( 66.4^{\circ} \)
\( 39.3^{\circ} \)

1103021412

Level: 
B
The figure shows a rectangular trapezium whose bases have lengths of \( 21\,\mathrm{cm} \) and \( 15\,\mathrm{cm} \), and the longer arm is \( 10\,\mathrm{cm} \) long. Calculate the sine of the smallest interior angle of the trapezium.
\( 0.8 \)
\( 0.6 \)
\( 53.13^{\circ} \)
\( 36.87^{\circ} \)

1103021410

Level: 
B
Given the isosceles trapezium \( ABCD \): \( |AB| = 15\,\mathrm{cm} \), \( |AC| = 12\,\mathrm{cm} \) and the measure of the angle \( ACB \) is \( 90^{\circ} \). The diagonals intersect at point \( S \). Express the measure of \( \measuredangle BSC \). Round to two decimal places.
\( 73.74^{\circ} \)
\( 106.26^{\circ} \)
\( 53.13^{\circ} \)
\( 26.15^{\circ} \)

1103021409

Level: 
B
Give the area of the isosceles trapezium \( ABCD \), if \( AB \parallel CD \), \( |CD| = 4\,\mathrm{cm} \), the height \( v = 16\,\mathrm{cm} \) and the measure of \( \measuredangle CAB \) is \( 30^{\circ} \). Round the result to units.
\( 443\,\mathrm{cm}^2 \)
\( 10\,\mathrm{cm}^2 \)
\( 411\,\mathrm{cm}^2 \)
\( 143\,\mathrm{cm}^2 \)

1103021408

Level: 
B
Given the isosceles trapezium \( ABCD \), where \( |AB| = 12\,\mathrm{cm} \), \( |BC| = 2\,\mathrm{cm} \), \( |CD| = 14\,\mathrm{cm} \) and \( |AD| = 2\,\mathrm{cm} \), determine the measure of \( \measuredangle ABC \).
\( 120^{\circ} \)
\( 30^{\circ} \)
\( 180^{\circ} \)
\( 150^{\circ} \)

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.
\( 30^{\circ} \)
\( 60^{\circ} \)
\( 26.57^{\circ} \)
\( 45^{\circ} \)