Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 5 Geometry
Problem
1) A square is outlined in string and has an area of 64 square units. If you take the string to make a regular octagon that has the same perimeter as the square, how long is one side of the octagon?
2) The quadrilateral ABCD has parallel sides AB and DC. Side AD is perpendicular to side AB. What is the sum of the angles at B and C?
3) 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?

Problem
4) Right triangle ABC shown in the figure has a right angle at B and a 50oangle at A. Reflect triangle ABC over side BC to create a new larger shape made up of two triangles. What's the measure of the new big angle at vertex C?
5) Rita wants to draw a square on a coordinate graph. The square is 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.