Geometry — Quiz 6

Questions in this quiz (7)

1. Every side of a regular hexagon is 1. Find the distance from the center to any side.

   • $$\frac{3}{4}$$
   • $$\frac{3}{2}$$
   • $$\frac{\sqrt{3}}{2}$$
   • $$\frac{\sqrt{2}}{6}$$

2. Every interior angle of a large regular polygon is 150°. How many sides does the polygon have?

   • 30
   • 15
   • 12
   • 16

3. In triangle $$\triangle PQR$$, points $$M$$ and $$N$$ are the midpoints of sides $$PQ$$ and $$PR$$ respectively. If $$QR = 12$$, find the length of segment $$MN$$.

   • 6
   • 4
   • 8
   • 9

4. The two diagonals of a rectangle PQRS intersect at point M. In addition, $$\angle PMQ = 130^\circ$$. Find the measure of $$\angle PSM$$.

   • $$25^\circ$$
   • $$65^\circ$$
   • $$45^\circ$$
   • $$60^\circ$$

5. A vertical stick 40 m long casts a shadow 20 m long on the ground. At the same time, a tower casts a shadow 50 m long on the ground. The height of the tower is:

   • 100
   • 50
   • 40
   • 60

6. Suppose rectangle $$WXYZ$$ is split into two congruent trapezoids by diagonal segment $$UV$$. If $$\angle UVZ=60^\circ$$, $$WU=3$$ units, and $$ZV=5$$ units, what is the area of rectangle $$WXYZ$$?

   • $$20\sqrt{3}$$
   • $$3\sqrt{3}$$
   • $$5\sqrt{3}$$
   • $$10\sqrt{3}$$

7. If angle N is a right angle, what is the value of $$x$$?

   • $$1$$
   • $$-\frac{1}{2}$$
   • $$\frac{1}{2}$$
   • $$-1$$