Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 6 Geometry
Problem
1) ABCD and MNOP are squares. M, N, O, and P are at midpoints of the four sides of the square ABCD. If MN is 8 inches, what is the area of the square ABCD?
2) Jenny build a pyramid out of sugar cubes to model a Mayan pyramid. Each layer is a solid square of sugar cubes and the pyramid looks the same on all four sides. The bottom layer shows 10 cubes along each side. The next layer shows 9 cubes along each side and so on ending with one cube on top. Jenny paints all the surfaces of the pyramid that are showing. How many cubes have no paint on them?

3) A cubic shaped fish tank is 40 inches tall. One quarter of the tank is filled with water. A metallic cube is added to the tank that has edge length 30 inches. How much water in cubic inches is needed to fill the tank the rest of the way?

Problem
4) A rectangular garden 30 m by 40 m will have a concrete walkway of uniform width all the way around. Find what width of the walkway to the nearest foot so that the area of the walkway equals the area of the garden.

5) The geometry net shown folds to a cube with a missing face. On this figure mark with an x two edges where the final square can be placed so that the net will fold to a cube with no missing faces.