Perimeter, Area & Volume — Quiz 7

Questions in this quiz (7)

1. In the standard $$(x,y)$$ coordinate plane, the region bounded by the lines $$x=d$$, $$y=0$$, and $$y=3x$$ has an area of $$27$$. What is the value of $$d$$?

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

2. A circular pond overlaps with a rectangular garden. The area of the pond is $$3$$ times the area of the garden. If the overlapping region is removed, the area of the remaining part of the pond is $$40$$ square meters more than the remaining part of the garden. What is the total area of the garden in square meters?

   • $$30$$
   • $$15$$
   • $$20$$
   • $$25$$

3. A carpenter has $$30$$ triangular wooden planks, each shaped like a right triangle with side lengths of $$5$$ inches, $$12$$ inches, and $$13$$ inches. He wants to use these planks to completely cover a rectangular table that is $$15$$ inches wide. What is the maximum possible height, in inches, of the table that can be fully covered with these $$30$$ triangular planks?

   • $$60$$
   • $$90$$
   • $$9000$$
   • $$650$$

4. A circular park has a walking path that follows an arc along its edge. The center of the park is labeled as $$C$$, and two points $$P$$ and $$Q$$ lie on the circle, forming an arc $$PQ$$. The sector $$CPQ$$ has an area of $$150\pi$$ square meters, and the central angle $$\angle PCQ$$ measures $$45^\circ$$. What is the length of arc $$PQ$$, in meters?

   • $$5\pi \sqrt{3}$$
   • $$20\sqrt{3}$$
   • $$40\pi \sqrt{3}$$
   • $$40\pi$$

5. A rug is $$m$$ yards long and $$n$$ feet wide. How many dollars will it cost if the rug sells for $$r$$ cents per square foot?

   • $$\frac{3mnr}{100}$$
   • $$mnr$$
   • $$\frac{mnr}{100}$$
   • $$\frac{mnr}{3}$$

6. Consider the following figure. Calculate the distance FG. If you know that the perimeter of triangle EFG is equal to 13.4, compute the length of segment FG.

   • 5.6
   • 13.4
   • 7.8
   • 3.6

7. In the shown figure, ABCD is a square and RST is an equilateral triangle. If the area of the shaded region is 3 times the area of the white triangle and if RT=2, then what is AB?

   • $$\sqrt3$$
   • $$2\sqrt[4]{3}$$
   • $$2\sqrt3$$
   • $$4\sqrt3$$