Geometry — Quiz 1

Questions in this quiz (10)

1. What is the side length of an equilateral triangle whose altitude is 6?

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

2. Line PR is a diagonal of square PQRS. What is the sine of angle PRQ in terms of the side length of the square?

   • $$\frac{\sqrt{2}}{3}$$
   • $$\frac{\sqrt{2}}{2}$$
   • $$\frac{1}{2}$$
   • $$\frac{1}{4}$$

3. One leg of a right triangle is 6 and its hypotenuse is 12. What is the size of its smallest angle?

   • $$60^\circ$$
   • $$20^\circ$$
   • $$90^\circ$$
   • $$30^\circ$$

4. One leg of a right triangle is 8 and the hypotenuse is 13. What is the length of the other leg?

   • $$\sqrt{233}$$
   • $$\sqrt{105}$$
   • $$233$$
   • $$105$$

5. What is the area of a 30–60–90 triangle whose shortest leg is 4?

   • $$2\sqrt{2}$$
   • $$8\sqrt{3}$$
   • $$4\sqrt{3}$$
   • $$16\sqrt{3}$$

6. A 5-foot tall girl stands in the shadow of a 15-foot tall tree. If the girl is standing 4 feet from the base of the tree, what is the length of the tree's shadow?

   • 10
   • 15
   • 60
   • 12

7. How large (in degrees) is the exterior angle of a regular octagon (all 8 sides are congruent)?

   • 65
   • 135
   • 115
   • 45

8. How large (in degrees) is the interior angle of a regular hexadecagon (all 16 sides are congruent)?

   • 202.5
   • 250
   • 110
   • 157.5

9. If a rectangle has an area of 84 units and a width of 7 units, what is the length of its diagonal?

   • $$\sqrt{12}$$
   • $$\sqrt{193}$$
   • $$12$$
   • $$12\sqrt{2}$$

10. Given a triangle ABC. Which equation shows how the angles $$a$$, $$b$$, and $$c$$ are related?

    • $$a +b + c = 360$$
    • $$a = b + c$$
    • $$a +b = 180 - c$$
    • $$a +b + c = 90$$