Grades 9-10 Video Solutions 2026-2026_9-10

Video Transcription

Video Summary

In equilateral triangle \(PQR\), \(S\) is the midpoint of \(PR\), so triangle \(PQS\) has half the area of \(PQR\). The line through the midpoint of \(QS\) is parallel to \(PR\), creating a smaller similar triangle at the top with side lengths half as large, so its area is \(1/4\) of triangle \(PQS\). The shaded region is triangle \(PQS\) minus this small triangle, giving \(3/4\) of \(PQS\). Since \(PQS\) is half of \(PQR\), the shaded fraction of the whole triangle is \(\frac{3}{8}\).

Keywords

equilateral triangle

area fraction

similar triangles

midpoint

shaded region