Area & Perimeter & Volume — Geometry and Trigonometry

Questions in this quiz (9)

1. Each side of a square has a length of $$27$$. What is the perimeter of this square?

   • $$27$$
   • $$729$$
   • $$27\sqrt{2}$$
   • $$108$$

2. The perimeter of triangle $$XYZ$$ is $$28$$ inches. The length of side $$XY$$ is $$9$$ inches, and the length of side $$XZ$$ is $$8$$ inches. What is the length, in inches, of side $$YZ$$?

   • $$8$$
   • $$11$$
   • $$19$$
   • $$17$$

3. The width of a rectangle is $$9$$ centimeters. The length of the rectangle is $$35$$ centimeters longer than the width. What is the area, in square centimeters, of this rectangle?

   • $$315$$
   • $$81$$
   • $$410$$
   • $$396$$

4. A triangle has a base length of $$36$$ centimeters and a height of $$50$$ centimeters. What is the area, in square centimeters, of the triangle?

   • $$1800$$
   • $$1500$$
   • $$1200$$
   • $$900$$

5. Each base of a right rectangular prism has a length of 15 inches and a width of $$12$$ inches. The prism has a volume of $$2700$$ cubic inches. What is the height, in inches, of the prism?

   • $$180$$
   • $$225$$
   • $$15$$
   • $$30$$

6. Triangle $$PQR$$ and triangle $$STU$$ are similar triangles, where $$PQ$$ and $$ST$$ are corresponding sides. If $$ST=3PQ$$ and the perimeter of triangle $$PQR$$ is $$18$$, what is the perimeter of triangle $$STU$$?

   • $$6$$
   • $$12$$
   • $$36$$
   • $$54$$

7. In the figure shown, triangle $$PQR$$ is similar to triangle $$XYZ$$, where $$P$$ corresponds to $$X$$ and $$R$$ corresponds to $$Z$$. The length of $$PR$$ is $$18$$, and the perimeter of triangle $$PQR$$ is $$54$$. The length of $$XZ$$ is $$72$$. What is the perimeter of triangle $$XYZ$$?

   • $$96$$
   • $$108$$
   • $$192$$
   • $$216$$

8. What is the volume of a cone with a circular base if the radius is $$4$$ units and the height is $$9$$ units?

   • $$\frac{1}{3}\pi$$
   • $$12\pi$$
   • $$3\pi$$
   • $$48\pi$$

9. A hexagonal prism has a height of $$8$$ inches. The area of each hexagonal base is $$30$$ square inches. What is the volume of the hexagonal prism?

   • $$120$$
   • $$240$$
   • $$360$$
   • $$480$$