Problem
GEO-B1-M06-P020 A Point on a Cevian
#20
★★★☆☆ Level 3 of 5
The area of triangle \(ABC\) is \(90\). Point \(D\) lies on \(BC\), and point \(E\) lies on \(AD\), with \(AE:ED=1:2\). Find \(S_{BCE}\).
Compare the heights from \(E\) and \(A\) to base \(BC\).
Triangles \(BCE\) and \(BCA\) have common base \(BC\). Since \(AE:ED=1:2\), point \(E\) is \(\frac{1}{3}\) of the way from \(A\) to \(D\), where \(D\) lies on \(BC\). Therefore the height from \(E\) to \(BC\) is \(\frac{2}{3}\) of the height from \(A\). Hence \(S_{BCE}=\frac{2}{3}\cdot90=60\).
A problem on how height changes along a segment toward the base.