Area Word Problems

This kind of word problem involves a shape (usually a rectangle or triangle) that you know the area of and are asked to find the dimensions. For the rectangle, you have to find the length and width. For the triangle, the base and height. Here is an example.

Can two rectangles with the same perimeter have different areas?

The length of the top of a table is 5m greater than the width. The area is 84 square meters. Find the dimensions of the table. 

The background for all of these problems is knowing the area formulas for the basic shapes.

adapted from http://domeprep.com/sat-act-prep/sat-course/on-demand/study-guides/basic-geometry

 Let's look at some examples. 

• Example 1: The table probrem (from above)
• Example 2: A Basic Triangle Problem

Now try a few on your own.

• Practice Problem 1: There is a rectangular parking lot that has a length 5m longer than it's width. If the area of the parking lot is 84 square meters, what are the width and the length.  [here is the solution, don't peak until you've tried it.]
• Practice Problem 2: A triangular traffic island has a base half as long as its height. The island has an area of 36 square meters. Find the base and the height.  [here is the solution, don't peak until you've tried it.]
• Practice Problem 3: An architect has allocated a rectangular space of 420 square feet for a square dining room and a 23ft wide kitchen. Find the dimensions of each room. [here is the solution, don't peak until you've tried it.] 

• Practice Problem 4: The height of a triangular sail is 5 ft greater than its base. If the area of the sail is 42 square feet. Find the length of the height and the base. [here is the solution, don't peak until you've tried it.]
• Practice Problem 5: The outside of a picture frame measures 14 inches by 20 inches. If 80 square inches of the picture shows, find the thickness of the frame. [here is the solution, don't peak until you've tried it.]