Trigonometry & Triangles; Showing How Two "Same" Things Are Not Equal

This activity uses the basic trigonometric ratio to show that it is possible for shapes to have equal measures but still have different areas.

Using cell phones as an example, the students will compare two different cell phones that have the same screen size, but different aspect ratios, and prove that the same screen size does not necessarily equate to the same amount of screen area. They will find the length of the sides using all three trigonometric functions, and then calculate the area. Then they will be able to compare cell phone #1 to cell phone #2, and determine which has the greater amount of screen area, despite having the same screen size.