2010015004
Level:
B
The isosceles trapezium \( ABCD \) is in the picture. The measure of the angle \( DAB \) is \( 60^{\circ} \). Determine the measure of the angle \( BCD \).
\( 120^{\circ} \)
\( 60^{\circ} \)
\( 110^{\circ} \)
\( 150^{\circ} \)
Polygons
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.
\( 40.96\,\mathrm{cm} \)
\( 28.68\,\mathrm{cm} \)
\( 71.41\,\mathrm{cm} \)
\( 46.98\,\mathrm{cm} \)
2010015002
Level:
A
\( KLMN \) is a square. Determine the degree measure of the angle \( NRS \) if the measure of the angle \( LSR \) is \( 110^{\circ} \).
\( 155^{\circ}\)
\( 120^{\circ} \)
\( 110^{\circ} \)
\( 135^{\circ} \)
2010015001
Level:
A
The side lengths of the rectangle \( ABCD \) are in the ratio \( AB: BC=4:3 \). Give the degree measure of the angle \( ASB \). Round the result to two decimal places.
\( 106.26^{\circ} \)
\( 73.74^{\circ} \)
\( 104.26^{\circ} \)
\( 75.74^{\circ} \)
2010011205
Level:
A
A diagonal of a rectangle has length of \( 26\,\mathrm{cm} \) and the perimeter of the rectangle is \( 68\,\mathrm{cm} \). Find the difference of the length and the width of the rectangle in centimeters.
\( 14 \)
\( 20 \)
\( 24 \)
\( 28\)
2010006705
Level:
A
The perimeter of a rectangle is \(22\, \mathrm{cm}\).
The diagonal of this rectangle is \(\sqrt{65}\, \mathrm{cm}\).
Find the sides of the rectangle.
\(7\, \mathrm{cm}\)
and \(4\, \mathrm{cm}\)
\(14\, \mathrm{cm}\)
and \(8\, \mathrm{cm}\)
\(6\, \mathrm{cm}\)
and \(5\, \mathrm{cm}\)
\(10\, \mathrm{cm}\)
and \(1\, \mathrm{cm}\)
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 \(KLMN\)?
\(100\,\mathrm{cm}^2\)
\(80\,\mathrm{cm}^2\)
\(120\,\mathrm{cm}^2\)
\(50\,\mathrm{cm}^2\)
2000006007
Level:
B
In the trapezoid \(KLMN\), \(|KS|=2|SM|\). The area of the triangle \(KSN\) is \(14\,\mathrm{cm}^2\). What is the area of the trapezoid \(KLMN\)?
\(63\,\mathrm{cm}^2\)
\(56\,\mathrm{cm}^2\)
\(42\,\mathrm{cm}^2\)
\(84\,\mathrm{cm}^2\)
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 \(KLMN\)?
\(36\,\mathrm{cm}^2\)
\(72\,\mathrm{cm}^2\)
\(18\,\mathrm{cm}^2\)
\(40\,\mathrm{cm}^2\)
2000006005
Level:
B
In the isosceles trapezoid \(ABCD\) is \(|AB|=|AC|\). The angle \(\alpha\) has the magnitude \(32^{\circ}\). What is the magnitude of the angle \(\delta\)?
\(106^{\circ}\)
\(120^{\circ}\)
\(148^{\circ}\)
\(74^{\circ}\)