B

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

1003021308

Level: 
B
Choose the wrong claim:
The sum of the opposite angles in a rectangle is \( 360^{\circ} \).
The sum of the interior angles of a convex n-gon is \( (n-2)\cdot180^{\circ} \).
If there is just one pair of sides parallel in a quadrilateral and the other side is perpendicular to them, then the quadrilateral is a right-angled trapezium.
At least one of the interior angles in a trapezium is obtuse.

1003019206

Level: 
B
Adam and Eve met at the disco. They agreed to meet the next day at the same location sometime between \( 1 \) p.m. and \( 2 \) p.m. Both of them will arrive independently at random times within the hour. Adam is greatly interested in the meeting, therefore he is willing to wait for Eve even up to half an hour, while Eve is willing to wait for Adam for \( 10 \) minutes. What is the probability that they will meet during that hour?
\( \frac{19}{36}\doteq 0{.}5278 \)
\( \frac{17}{36}\doteq 0{.}4722 \)
\( \frac{11}{36}\doteq 0{.}3056 \)
\( \frac{27}{36}=0{.}75 \)

1003019204

Level: 
B
Inside a circle is inscribed a square. A point is chosen at random from inside the circle. What is the probability that this point is located also in the square?
\( \frac2{\pi}\doteq 0{.}6366 \)
\( \frac{\pi}4\doteq 0{.}7854 \)
\( \frac{\sqrt{2}}{\pi}\doteq 0{.}4502 \)
\( \frac{\sqrt{2}}{2\pi}\doteq 0{.}2251 \)