Polygons

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.

9000121708

Level: 
A
Consider a square \(ABCD\) and a point \(E\) on the side \(BC\) such that the angle \( BAE\) has measure \(20^{\circ }\). The point \(F\) is on the side \(CD\) and the length of \(AF\) equals to the length of \(AE\) (i.e. the triangle \(AEF\) is isosceles with \(AF\) and \(AE\) of equal length). Find the measure of the angle \( AEF\).
\(65^{\circ }\)
\(45^{\circ }\)
\(50^{\circ }\)
\(70^{\circ }\)

9000121802

Level: 
B
Consider a regular polygon with the central angle of \(20^{\circ }\). In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find the number of vertices of this polygon.
\(18\)
\(9\)
\(20\)
\(15\)

9000121807

Level: 
B
In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon, the blue angle is the interior angle of the polygon. Suppose we consider a regular polygon with the central angle of \(40^{\circ}\), then find the measure of the interior angle of this polygon.
\(140^{\circ }\)
\(80^{\circ }\)
\(200^{\circ }\)
\(120^{\circ }\)