Triangle Geometry Practice
Here are a couple of problems I saved a while back from the Drexel University Math Forum:
1. A square with side length s is inscribed in an equilateral triangle of side length t. t = ks. Find k, expressed as a fraction in simplest radical form.
2. A regular hexagon and an equilateral triangle are both inscribed in the same circle so that the hexagon and the triangle share three vertices. The radius of the circle is 8 units. What is the area of the region between the two polygons?