mad hatter practice problems
i'm going over same previous problems from the mad hatter math contest, and i need help with a few.
28. Two congruent 30-60-90 triangles are placed so that they overlap partly and their hypotenuses coincide. If the hypotenuse of each triangle is 12, the area common to both triangles is...?
--question: i don't understand how the triangles have coinciding hypotenuses but still overlap slightly---
36. A circle is inscribed in an equilateral triangle, a square is inscribed in the circle. The ratio of the areas of the triangle to the square is...?
38. If the sum of all the angles except one of a convex polygon is 2190 degrees, then the number of sides of the polygon must be...?
44. The perimeter of an isosceles right triangle is 2p, its area is...?