Math 60: Geometry

Math 60: Geometry

Where to look in your ALEKS pie: All the material is located in your "Geometry" slice.

Directions: You may use a calculator for the computations in this workbook, but you should show how you set each formula up. Be sure to include the correct units with your answers. You may use the value 3.14 for π. Circle your answers, and if an exercise has more than one part, label each answer clearly. Round to the nearest tenth.

Formulas: If you're not sure what a variable stands for, please ask.

AREA VOLUME

Rectangle: A=LW Rectangular prism (box): V=LWH

Triangle: A=12bh Cylinder: V=πr2h

Trapezoid: A=12h(b1+b2) PERIMETER/CIRCUMFERENCE

Circle: A=πr2 Rectangle: P=2L+2W

Circle: C=πd or C=2πr

Exercise 1: Find the area and perimeter of an index card measuring 3 inches by 5 inches.

Exercise 2: Find the area of the windshield shown below.

Exercise 3: Find the area of the shaded figure below.

Exercise 4: Your circular kitchen tabletop measures 5 feet across. What is its area? If it is 2 inches thick, what is its volume (in cubic feet or cubic inches, your choice)?

Exercise 5: Find the area of the rug below, which is in the shape of a rectangle with a semicircle attached to each end.

Exercise 6: Find the volume of a closet that is 6 feet wide, 3 feet deep, and 7 feet tall.

Exercise 7: Find the volume of a cylindrical water heater that measures 2 feet 6 inches in diameter and 5 feet in height.

Exercise 8: A running track is shaped like the perimeter of the rug in Exercise 5, but in this case the rectangle measures 360 feet by 160 feet. What is the distance around the track?

Note: The objective "Similar right triangles" will be particularly helpful here.

Exercise 9: Given that the two triangles below are similar, find x.

Exercise 10: A person 5 feet 3 inches tall casts a 6-foot shadow. At the same time of day, a lamppost casts an 18-foot shadow. How tall is the lamppost, as a mixed measurement (i.e., in feet and inches)?