Stephani Eckelkamp


 Fun with Area

~~Exploration of the area of triangle constructed by the three medians in relation to the original triangle~~


What does it look like?  Here are two different ways of viewing this problem




Explore this link to find possible ratios between area and perimeter of these triangles.


Notice that the area of the triangle formed by the medians is ¾ the area of the original triangle. 


Can we prove this relationship between these two triangles?



First we must look at point U and prove that it is the midpoint of line segment BY.

Try to construct this proof on your own. 

Click here to see proof


Now that we know that U is the midpoint, we can begin to explore the relationship between the two areas.

Can you prove that these areas have a ratio of 3/4 ?

Click here to see proof