IMO Practice Test — Areas of Parallelograms and Triangles

ABCD is a parallelogram. A point E is chosen randomly inside the parallelogram. What is the sum of the areas of Triangle EAB and Triangle ECD?

In a Triangle ABC, the medians AD, BE, and CF intersect at a single central point G (the centroid). If the total area of Triangle ABC is 72 sq cm, find the area of the small sub-triangle AGB.

ABCD is a trapezium where side AB runs parallel to side CD. The diagonals AC and BD intersect each other at a central point O. Compare the areas of Triangle AOD and Triangle BOC.

In a Triangle ABC, points D and E are marked on side BC such that the side is split into three equal parts (BD = DE = EC). If the total area of Triangle ABC is 45 sq cm, find the area of Triangle ADE.

ABCD is a parallelogram. Points P and Q are the mid-points of sides BC and CD respectively. If you draw lines AP and AQ, what fraction of the total area of the parallelogram is the area of Triangle APQ?

In a Triangle ABC, D is the mid-point of side AB, and E is the mid-point of side AC. If a line segment DE is drawn, what is the ratio of the area of Triangle ADE to the area of the remaining quadrilateral DBCE?