Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem22

Levels 9&10 Video Solutions 2010 problem22

Video Transcription

Video Summary

The problem involves calculating the shaded area percentage in an equilateral triangle divided by lines parallel to its base, splitting each side into 10 equal segments. The total area is computed using \( \frac{\sqrt{3}}{4} \times (10s)^2 \). The shaded area is calculated by a series of subtractions and additions of smaller triangles' areas, each defined by \( n^2 \times \frac{\sqrt{3}}{4} \times s^2 \), where n is the triangle's segment count. After simplifying, the shaded area constitutes 45% of the total triangle area, making the answer 45% for the shaded portion.

Keywords

equilateral triangle

shaded area

area calculation

geometry problem

percentage