Grades 11-12 Video Solutions 2012-2012_11-12

Video Transcription

Video Summary

The problem involves calculating the area of triangle BEG within square ABCD with side length 2, where E and F are midpoints of sides AB and AD, respectively. Point G lies on CF such that 3CG = 2GF. By analyzing the geometric relationships, we first determine the area of a larger triangle within the square, observing that the base of triangle BEG is one-quarter of this larger triangle's base, and its height is four-fifths of that triangle's height. Thus, the area of triangle BEG is the product of the full area (4) times these fractions, resulting in an area of \(\frac{4}{5}\).

Keywords

triangle area

square ABCD

midpoints

geometric relationships

triangle BEG