Problem 90. Quadrilateral and Triangle areas, Midpoints. Level: High School, SAT Prep, College

In the figure below, given a triangle AED, M and N are the midpoints of cevians AC and DB respectively. If S1 and S are the areas of the triangle MEN and the quadrilateral ABCD respectively, prove that: Quadrilateralarea formula. Post a comment.

Quadrilateral area problem 

 

 

FACTS AND HINTS:

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."


1. CEVIAN: A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).


2. See Proposed Problem 87

Hint: See problem 87


2. See Proposed Problem 89

Hints: See proposed problem 89

 


 

Math problem 80 about quadrilateral area 

 

 

Home | Geometry | Search | Problems | All Problems | 81-90 | Email