Virginia Mathematics Teacher Fall 2016

So l ut i ons t o Spr i ng 2016 HEXA Cha l l enge Probl ems

April Challenge:

In a trapezoid ABCD. E is the midpoint of AB, F lies on CD, and EF is perpendicular to CD. Estimate the area of the trapezoid if EF= h and CD = b.

SOLUTION :

Draw line GE parallel to CD. G lies on line AD. H is the point of intersection between lines GE and BC. The area of the parallelogram GHCD is equal to the area of trapezoid ABCD, because the triangles EHB and AGE are equal to each other by angle-side-angle congruence condition. Thus the area of the trapezoid equals b times h.

May Challenge:

In a triangle ABC. AD and CF are medians, D is on BC and F is on AB. The medians intersect at O. What is the ratio of the triangular areas DOF to ABC?

Virginia Mathematics Teacher vol. 43, no. 1

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