Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 7 Geometry
Problem
1) A wooden rectangular block measuring 9 inches by 12 inches by 16 inches is painted blue. The block is then cut up into 1-inch cubes. How many of the 1-inch cubes have blue on exactly one side?

2) In right triangle ABC, the measure of angle 1 is 40% of the measure of angle 2. What is the measure of angle 3?
3) Mrs. Frieze is designing a geometric border to go around the top of her classroom wall. It's a repeating design and you can see a part of it in the diagram. The indicated angles at P are congruent and the indicated angles at Q are congruent. The angles at A and B are 90 degree angles. What is the length of QC?

Problem
4) Demi is charged with finding the dimensions of a can that will hold twice as much as the 9 by 12 cm can as shown but have the same proportions. Her first step is to try a simpler problem. She computes the dimensions of the rectangle that would have twice the area but the same proportions as the shaded rectangle shown with base 9 cm and height 12 cm. What is the ratio between the height of the bigger rectangle to 12?

5) Triangle RST is the image of triangle ABC under a reflection and a translation. What is the translation? Describe it in terms of units moved up or down and units moved left or right.