Polygons

1103054907

Level: 
C
The picture shows a kite. Give the measures of all interior angles \( \alpha \), \( \beta \), \( \gamma \) and \( \delta \).
\( \alpha = 124^{\circ} \), \( \beta = 108^{\circ} \), \( \gamma = 20^{\circ} \), \( \delta = 108^{\circ} \)
\( \alpha = 124^{\circ} \), \( \beta = 108^{\circ} \), \( \gamma = 124^{\circ} \), \( \delta = 108^{\circ} \)
\( \alpha = 124^{\circ} \), \( \beta = 72^{\circ} \), \( \gamma = 20^{\circ} \), \( \delta = 72^{\circ} \)
\( \alpha = 124^{\circ} \), \( \beta = 108^{\circ} \), \( \gamma = 72^{\circ} \), \( \delta = 83^{\circ} \)

1103054910

Level: 
C
In the kite \( ABCD \), \( |AB| = |BC| = 12\,\mathrm{cm} \), \( |CD| = |DA| = 6\,\mathrm{cm} \), and the measure of \( \measuredangle DAB \) is \( 120^{\circ} \). Calculate the area of the kite.
\( 36\sqrt3\,\mathrm{cm}^2 \)
\( 24\sqrt3\,\mathrm{cm}^2 \)
\( 18\sqrt3\,\mathrm{cm}^2 \)
\( 36\,\mathrm{cm}^2 \)

2010018004

Level: 
C
A rectangle-shaped land has dimensions \(5 \times 8\,\mathrm{cm}\) on a map with scale \(1:500\). The owner increased the size of his land by buying some land from his neighbor. The new land has dimensions \(7\times 9\,\mathrm{cm}\) on the map. Find the actual increase of the perimeter of the land (i.e. find the increase in the length of the fence required to enclose the whole land). Give your answer in meters.
\(30\,\mathrm{m}\)
\(15\,\mathrm{m}\)
\(40\,\mathrm{m}\)
\(60\,\mathrm{m}\)

9000124502

Level: 
C
A rectangle-shaped land has dimensions \(3\times 5\, \mathrm{cm}\) on a map with scale \(1\colon 2\: 000\). The owner increased the size of his land by buying some land from his neighbor. The new land has dimensions \(4\times 5\, \mathrm{cm}\) on the map. Find the actual increase of the perimeter of the land (i.e. find the increase in the length of the fence required to enclose the whole land). Give your answer in meters.
\(40\, \mathrm{m}\)
\(20\, \mathrm{m}\)
\(80\, \mathrm{m}\)
\(10\, \mathrm{m}\)

9000150502

Level: 
C
Two hotels and a lake are in a satellite photo. The distance between the hotels is \(400\, \mathrm{m}\) which is \(4\, \mathrm{cm}\) in the photo. The area of the lake in the photo is \(30\, \mathrm{cm}^{2}\). Find the real area of the lake.
\(3\cdot 10^{5}\, \mathrm{m}^{2}\)
\(3\cdot 10^{1}\, \mathrm{m}^{2}\)
\(3\cdot 10^{3}\, \mathrm{m}^{2}\)
There is not enough information to solve this problem.