Grades 11-12 Video Solutions 2025-2025_11-12

Video Transcription

Video Summary

In this Math Kangaroo problem for grades 11-12, the challenge is to find the length of OR given a quarter circle OPQ and a triangle OPR with equal shaded areas. By focusing on combining unshaded and shaded areas, the problem simplifies to comparing areas of known shapes: a quarter circle and a triangle. The calculations involve equating the triangle's area \( R \times \text{height} / 2 \) to that of the quarter circle \( R^2 \pi / 4 \). Solving this results in the formula \( H = R \pi / 2 \), corresponding to answer choice A: \( \frac{\pi r}{2} \).

Keywords

Math Kangaroo

quarter circle

triangle area

equating areas

formula derivation