Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 7 Geometry
Problem
1) Trapezoid ABCD is similar to trapezoid EBFG. Find AD.
2) In the figure, line P is parallel to line R. Angles of measures 40 degrees and 75 degrees are marked. What is the measure of angle x?
3) The points of an isosceles triangle are A=(2,3), B=(3,1), and C=(1,1). If you rotate the triangle 180 degrees about the origin and then reflect the triangle across the x-axis, what are the new coordinates for A,B, and C?

Problem
4) If a square cake with side length 8 inches serves 4 people, how many people would be able to get an equivalent serving from a 12 inch diameter circular cake? Both cakes are the same height.
5) A circular cone can be created by joining the two straight edges of the shown section of a circle with central angle 90 degrees and radius 5 centimeters. What is the diameter of the created cone? (The diameter of a cone is the diameter of the circular opening where it is the widest.)