Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 8 Geometry
Problem
1) The area of a square is the same as the area of a rectangle. The rectangle has a width of 6 units. The side of the square has length S. The rectangle has length L and is 4 times as long as S. What is the area of the square in square units?

2) Write the letters M, T, and H on figure 2 so that when the figure is folded into a box, it will spell MATH around the sides of the box. Figure 1 shows the correct placement of the letters

Problem

3) The hexagon shown has line of symmetry BE. The measure of angle FAB is 150 degrees, the measure of angle ABC is 114 degrees and the measure of angle DEF is 100 degrees. What is the measure of angle CDE?
4) There is a translation and a rotation taking vertices E, F, and G to R, S, and T. Where does vertex H go under this translation and rotation? Give your answer as a coordinate pair.
5) The latitude of a point, P, on the earth's surface is the measure of angle PCE, where C is the center of the earth and E is the point on the equator closest to P, see Figure 1. One night Joey measures the angle between a vertical pole at P and the direction of the North Star to be 50 degrees and plots this on the diagram in Figure 2. If the line from the center of the earth through the North Pole to the North Star is parallel to line of sight from P to the North Star, then what is the latitude of point P?