Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 5 Geometry
Problem
1) A parallelogram has vertices at (0, 0), (5, 2), and (1, 3).
The fourth vertex has positive coordinates. What are they?

2) Jenny build a pyramid out of sugar cubes to model a Mayan pyramid. Each layer is a solid square of sugar cubes and the pyramid looks the same on all four sides. The bottom layer shows 10 cubes along each side. The next layer shows 9 cubes along each side and so on ending with one cube on top. Jenny paints all the surfaces of the pyramid that are showing. How many cubes have no paint on them?

3) At six o'clock the angle between the hour and minute hands on a clock is 180 degrees. What is the angle between the hour and minute hands on the clock at 6:30 pm? Assume that both hands move at a constant rate.

Problem
4) Parallelogram ABCD has line of symmetry AC and has an angle of 120o at angle BAD. What kind of triangle is triangle ABC?

5) Two of the vertices of a parallelogram that contains trapezoid ABCD are (1,3) and (2,1). The parallelogram has twice the area of trapezoid ABCD, and its coordinates are positive. What are its other two vertices?