Polygons

2000006004

Level: 
B
In the parallelogram \(ABCD\), the side \(AB\) is \(10\,\mathrm{cm}\) long, the diagonal \(AC\) measures \(15\,\mathrm{cm}\). The distance of the vertex \(D\) from the diagonal \(AC\) is \(2\,\mathrm{cm}\). What is the distance of the vertex \(D\) from the side \(AB\)?
\(3\,\mathrm{cm}\)
\(4\,\mathrm{cm}\)
\(5\,\mathrm{cm}\)
\(6\,\mathrm{cm}\)

2000006006

Level: 
B
The bases of the trapezoid \(KLMN\) are \(12\,\mathrm{cm}\) and \(4\,\mathrm{cm}\) long. The area of the triangle \(KMN\) is \(9\,\mathrm{cm}^2\). What is the area of the trapezoid \(KLMN\)?
\(36\,\mathrm{cm}^2\)
\(72\,\mathrm{cm}^2\)
\(18\,\mathrm{cm}^2\)
\(40\,\mathrm{cm}^2\)

2000006008

Level: 
B
The trapezoid \(KLMN\) has bases \(15\,\mathrm{cm}\) and \(10\,\mathrm{cm}\) long. The point \(T\) is any point of the longer base. The area of the triangle \(MNT\) is \(40\,\mathrm{cm}^2\). What is the area of the trapezoid \(KLMN\)?
\(100\,\mathrm{cm}^2\)
\(80\,\mathrm{cm}^2\)
\(120\,\mathrm{cm}^2\)
\(50\,\mathrm{cm}^2\)

2010015003

Level: 
B
\( ABCD \) is a rhombus, the measure of the angle \( DAB \) is \(70^{\circ}\) and the shorter diagonal \( u = 50\,\mathrm{cm} \). Determine the height \(v\) of the rhombus. Round the result to two decimal places.
\( 40.96\,\mathrm{cm} \)
\( 28.68\,\mathrm{cm} \)
\( 71.41\,\mathrm{cm} \)
\( 46.98\,\mathrm{cm} \)

2010015005

Level: 
B
Given the isosceles trapezium \( ABCD \), where \( |AB| = 12\,\mathrm{cm} \), \( |BC| = 4\,\mathrm{cm} \), \( |CD| = 16\,\mathrm{cm} \), and \( |AD| = 4\,\mathrm{cm} \), determine the measure of \( \measuredangle BCD \).
\( 60^{\circ} \)
\( 70^{\circ} \)
\( 45^{\circ} \)
\( 120^{\circ} \)

2010015006

Level: 
B
The figure shows a rectangular trapezium whose bases have lengths of \( 19\,\mathrm{cm} \) and \( 14\,\mathrm{cm} \), and the longer arm is \( 13\,\mathrm{cm} \) long. Calculate the sine of angle \(\alpha\).
\( \frac{12}{13} \)
\( \frac{5}{13} \)
\( 22.62^{\circ} \)
\( 67.38^{\circ} \)