Oftentimes, you will be asked to solve problems involving geometric relationships or other shapes. For real-world problems, those geometric relationships mostly involve measurable attributes, such as length, area, or volume.

Sometimes, those problems will involve the perimeter or circumference, or the area of a 2-dimensional figure.

For example, what is the distance around the track that is shown?

Or, what is the area of the portion of the field that is covered with grass?

green elliptical running track

You may also see problems that involve the volume or surface area of a 3-dimensional figure.

For example, what is the area of the roof of the building that is shown?

building composed of a rectangular prism with a half-cylinder on top

Another common type of geometric problem involves using proportional reasoning.

For example, an artist created a painting that needs to be reduced proportionally for the flyer advertising an art gallery opening. If the dimensions of the painting are reduced by a factor of 40%, what will be the dimensions of the image on the flyer?

In this resource, you will investigate ways to apply a problem-solving model to determine the solutions for geometric problems like these.

A basic problem solving model contains the following four steps:

Step 1: Read, understand, and interpret the problem.

  • What information is presented?
  • What is the problem asking me to find?
  • What information may be extra information that I do not need?
Step 2: Make a plan.

  • draw a picture
  • look for a pattern
  • systematic guessing and checking
  • acting it out
  • making a table
  • working a simpler problem
  • working backwards
Step 3: Implement your plan.

  • What formulas do I need?
  • What information can I interpret from the diagram, table, or other given information?
  • Solve the problem.
Step 4: Evaluate your answer.

  • Does my answer make sense?
  • Did I answer the question that was asked?
  • Are my units correct?