Synthesis of Problems for Shaded Area Geometry Reasoning

Chris Alvin, Sumit Gulwani, Rupak Majumdar, Supratik Mukhopadhyay

Abstract: A shaded area problem in high school geometry consists of a figure annotated with facts such as lengths of line segments or angle measures, and asks to compute the area of a shaded portion of the figure. We describe a technique to generate fresh figures for these problems. Given a figure, we describe a technique to automatically synthesize shaded area problems. We demonstrate the efficacy of our synthesis techniques by synthesizing problems from fresh figures as well as figures from a corpus of problems from high-school geometry textbooks.