2001 Washington State Math Championship

Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth.

Geometry - Grade 8


1. A net for a cube is pictured. How many different (non-congruent) nets for a given cube are possible. [Warning: Not all possible arrangements of 6 squares form nets.]



2. The rectangle has an area of 108 square meters and a perimeter of 48 meters. How many meters is its longest dimension?

3. The over-crowded school puts all the students in one classroom that is 30 feet by 30 feet by 10 feet. Each student takes up 5 cubic feet, and there is no extra room for anyone else. How many students are in the school?

4. How many of the following symbols have rotation symmetry?

z v b a d f g h i [ N M J q W T Y $ \ % & ) _ ˆ

5. There are 5280 feet in a mile and 640 acres in a square mile. If acre is to be a rectangle whose dimensions are whole numbers of feet, how many different shapes are possible?

6. SQRD is a square. SBCA and RECT are rectangles. The diagonal of the largest rectangle goes through point R. If QR = 10 and RT = 4, what is the length of RE? [The figure is not drawn to scale.]



7. Two pieces of wire are of equal length. One wire is formed into the shape of a square, and the other is formed into the shape of a circle. What is the ratio of the area of the square to that of the circle?

8. The angles of a triangle are x, y, and z degrees. If and , how many degrees is z?

9. What is the length of the longest segment in the figure? [All triangles are right triangles.]



10. What is the area of a regular octagon with sides of length 2 inches?