Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 6 Geometry
Problem
1) A tangram puzzle has 7 shapes that can be put together to make a square as shown. If the side of the large square measures 4 inches, what is the area of the small square?
2) Rita wants to draw a square on a coordinate graph that's rotated a little bit around its center. She puts one vertex at (3,0), one vertex at (0, 1), and one vertex at (1, 4). Where will the last vertex go to complete the square? Use the coordinate graph provided.

Problem
3) Which of the following nets will correctly fold to make a triangular prism with one pointed tetrahedron side? (Think of a pointed three sided stake.)
4) In triangle ABC shown, AB is perpendicular to CB, and DE is parallel to AC. The angle at vertex A measures 42 degrees. What is the sum of the two angles labeled x and y?

5) A square is enlarged so as to increase its area by 300%. What is the ratio of the new side length to the old side length?