Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 6 Geometry

Problem

1) A rolling bike wheel makes 2 full rotations and moves a distance of 13.6 feet. What is the diameter of the wheel to the nearest inch?
Use = 3.14

2) In the diagram AB has length 8 cm and M is the midpoint of AB. DC is 1/3 the length of AB. The area of isosceles triangle DMC is 8 sq. cm. What is the area of isosceles trapezoid ABCD?

Problem

3) Julius is making a duffel bag out of a piece of canvas that measures 3 feet by 4 feet. It will be cylindrical with dimensions 2 feet long and diameter 1 foot. Disregard the seams. The two end pieces are sketched out. Sketch in the third piece. How much canvas will be left over after he cuts out the pieces? Express your answer to the nearest tenth of a square foot. Use = 3.14

4) In the floor plan for a museum 8 revolving security cameras are shown as dots. They cover the whole floor plan. The owner wants to know: Can fewer cameras be used and where would they need to be mounted? Indicate number and location on the diagram on the answer sheet.

5) Leo makes an octahedron by gluing together two pyramids along their bases. Its surface area is 16 square inches. Each triangle has a height of 2 inches. What is the surface area of one of the pyramids?