Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2011 Grade 8 Geometry
Problem
1) Farmer Judy is creating an oddly shaped rotationally symmetric raised garden bed. She needs by lumber to frame the bed. What is the perimeter of the bed? Express to the nearest foot? (The dashed lines are to indicate lengths and are not part of the framing.)
2) The diagram is a net for a pyramid with a square bottom with highest point above a corner of the square base. The outside solid lines are cut lines, the interior dotted lines are fold lines. If the side length of the square is 3 units, and the height of the pyramid, which is also its vertical edge, is 4 units, then what is the length of its longest edge C? Give an exact answer or express to the nearest hundredth.

Problem
3) A section of a map looks like the figure indicates. The roads are straight but meet at odd angles. Two of the angles are given. What is the measure of the angle labeled q?.
4) A pinwheel design is created by rotating the triangle shown about the origin to create 4 equally spaced copies each one having its interior in a different quadrant. The vertices all have integer coordinates. What are the coordinates of the copy of the triangle with interior in the fourth quadrant?
5) Jerry wants to recreate the drawing at right using a larger circle. A is the center of the circle and segment TC is congruent to segment TB. What is the fewest number of angles he needs to measure and still be able to compute the measure of all the angles in the drawing?