Problem
GEO-B1-M08-P004 Area and Ratio
#4
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), point \(D\) lies on \(BC\), and \(BD:DC=2:5\). The area of \(ABC\) is \(84\). Find \(S_{ABD}\).
Areas with a common height are in the ratio of the bases.
Triangles \(ABD\) and \(ABC\) have the common height from \(A\) to \(BC\). Since \(BD:BC=2:7\), we get \(S_{ABD}=\frac{2}{7}\cdot84=24\).
A warm-up on choosing areas instead of similarity.