Geometry — Quiz 7

Questions in this quiz (8)

1. In the standard $$xy$$-plane, three corners of a parallelogram are located at $$(1, 2), (5, 4), (2, -3)$$. Which of the following points could be the remaining corner?

   • $$(\frac{3}{2}, \frac{-1}{2})$$
   • $$(-2 , -5)$$
   • $$(\frac{1}{2}, \frac{-1}{2})$$
   • $$(\frac{-3}{2}, \frac{1}{2})$$

2. If the height of an equilateral triangle is 12, what is its area?

   • $$8\sqrt{3}$$
   • $$48\sqrt{3}$$
   • $$4\sqrt{3}$$
   • $$192\sqrt{3}$$

3. What is the area of ΔSRT in the following figure?

   • 144
   • 256
   • 78
   • 19.2

4. Taylor has $$P$$ feet of fencing. How many square feet of a rectangular region could it enclose if it is fenced in as a square?

   • $$\frac{P^2}{8}$$
   • $$\frac{P^2}{16}$$
   • $$\frac{P^2}{4}$$
   • $$\frac{P^2}{2}$$

5. Two sides of a triangle are 4 and 5. For what range of values of the third side $$x$$ is the triangle acute?

   • $$2$$ < $$x$$ < $$5$$
   • $$4$$< $$x$$ < $$6$$
   • $$3$$ < $$x$$ < $$7$$
   • $$3$$ < $$x$$ < $$\sqrt{41}$$

6. The vertices of $$\triangle ABC$$ are given in the standard $$(x, y)$$-coordinate plane as follows:$$A(-4, 8)$$, $$B(6, -2)$$, $$C(10, 10)$$What is the area, in square coordinate units, of $$\triangle ABC$$?

   • $$160$$
   • $$40$$
   • $$80$$
   • $$48$$

7. A triangle with angle measures $$30^\circ$$, $$60^\circ$$, and $$90^\circ$$ has a perimeter of $$36 + 12\sqrt{3}$$. What is the length of the longest side of the triangle?

   • $$12$$
   • $$36$$
   • $$42$$
   • $$24$$

8. In the figure shown, $$AB = \sqrt{45}$$ units, $$AC = 5$$ units, and $$CE = 25$$ units. What is the area, in square units, of triangle $$ADE$$?

   • $$150 \sqrt{5}$$
   • $$180 \sqrt{5}$$
   • $$15 \sqrt{5}$$
   • $$18 \sqrt{5}$$