Researchers have identified many ways that students think about rectangular area. However, research about students' understanding of triangle area is relatively scarce. Although it may seem simple to apply the triangle area formula, there is more to students' understanding of triangle area. In this dissertation, I obtained data to help answer the following questions: 1. What are high school geometry students' concept images of triangle base, height, and area? 2. How are high school geometry students' concept images of triangle base, height, and area related to one another? 3. How are triangle orientation, gravity, and triangle type related to high school geometry students' concept images of triangle base, height, and area? I used an interpretive lens called concept image and concept definition, introduced by Vinner and Hershkowitz (1980), as a tool to investigate students' interpretations of the triangle attributes (i.e., base and height) that are required to measure triangle area. My main data sources were a survey of 95 high school geometry students and semi-structured task-based interviews with 7 of those students. My study has potential benefits for researchers in the field of mathematics education both by demonstrating yet another use of the lens of concept image and concept definition, and by unveiling critical information about students' understanding of triangle area. Likewise, my study has potential benefits for practitioners by revealing the complexity of triangle attributes. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]