Problem
GEO-B1-M06-P010 Diagonal of a Trapezoid
#10
★★☆☆☆ Level 2 of 5
In trapezoid \(ABCD\), bases \(AD\parallel BC\), \(AD=15\), \(BC=9\). Diagonal \(AC\) divides the trapezoid into triangles \(ABC\) and \(ACD\). Find \(S_{ABC}:S_{ACD}\).
The heights to the parallel bases are equal to the distance between the bases.
Triangles \(ABC\) and \(ACD\) have bases \(BC\) and \(AD\) on parallel lines, and the heights to these bases equal the distance between the bases of the trapezoid. Therefore \(S_{ABC}:S_{ACD}=BC:AD=9:15=3:5\).
A good connection between trapezoids and areas.