How to Do Geometry Problems: Step-By-Step Solutions

Geometry Solutions

One of the most common types of geometry problems you'll be asked to solve is the kind in which you calculate a property of a shape. You'll be given some facts about a 2-dimensional object, like a rectangle or a circle, or a 3-dimensional object, like a cylinder or a cone. Then, you'll use that information to find a property of the shape, like perimeter or volume. To do this successfully, follow the steps below.

Step One

First, you'll need to assemble all of the facts that the problem gives you, like the length, height or diameter of the shape. In many cases, it helps if you draw a picture of the shape and label it with the information you're given.

Step Two

The next step is to identify what the problem is asking you to do. Do you need to figure out the shape's volume, perimeter, area or surface area?

Step Three

The third step is to identify the appropriate formula to calculate the value that's being asked for. Here are a few common formulas you may use:

Perimeter of a rectangle: 2(length) + 2(width)

Circumference of a circle: 2(3.14)(radius)

Area of a rectangle: length x width

Area of a circle: (3.14)(radius)^2

Area of a triangle: 1/2 x base x height

Volume of a rectangular prism: length x width x height

Step Four

Plug your information into the formula and solve it. Don't forget to check your work!

Step Five

Once you've solved your problem, there's one more step you need to complete before you're finished. One of the most common mistakes that students make when they're solving geometry problems is reporting their answers in the wrong type of unit. This can happen if you fail to notice that different parts of a problem are given in different units. For instance, the height of a rectangle might be given in meters, and its width might be given in centimeters. If you don't convert these measures into a single type of unit, you'll get the wrong answer.

It's also common for students to forget to report square or cubed units. If you're reporting area or surface area, your answer should be in square units, and if you're reporting volume, it should be in cubed units.