Grades 11-12 Video Solutions 2010-11&12 Video Solutions 2010 problem23

11&12 Video Solutions 2010 problem23

Video Transcription

Video Summary

The given problem involves calculating the area of a shaded triangle in square ABCD with side length 1. Points M, N, P, and Q are midpoints or intersections within the square. The solution involves computing areas of various smaller triangles and subtracting these to find the shaded triangle's area. Using coordinates and line equations, the values of alpha and beta—related to heights in the triangles—are determined. The area calculations conclude with the expression \(\frac{1}{15}\) as the area of the shaded triangle, which is the answer provided as choice P.

Keywords

shaded triangle

square ABCD

area calculation

midpoints

coordinates