Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 5 Geometry
Problem
1) The stained glass window design is a rhombus subdivided into four congruent rhombi. If the small angle at point M is 40o as shown then what is angle DAB?
2) A polygon has the two perpendicular lines of symmetry shown. One quarter of the interior of the polygon is the shaded trapezoid drawn in. Sketch the completed polygon and give its geometric name based on the number of sides or angles it has.

Problem
3) Two congruent isosceles triangles are joined together along a side to create a kite as shown. The perimeter of one of the triangles is 30 units. The lengths of the sides of the triangle are all whole numbers. What is the length of the longest side of the triangle if the perimeter of the kite is as long as possible?

4) Rosie builds a large cube out of sugar cubes. Her large cube has a width of 4 cubes, height of 4 cubes and length of 4 cubes. She wants to add one more layer of cubes all around to make an even larger cube that will have height, width and length 6 cubes. How many cubes does she need?
5) For triangle ABC shown on the coordinate grid what are the coordinates of a 4th point (D) that turns the triangle into a parallelogram?