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