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Washington State Math Olympiad
Hints and Solutions
2008 Grade 6 Geometry
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1) Toleen's math teacher makes a model of a solid rectangular prism out of white one centimeter
cubes to explore surface area and volume. She paints the entire outside surface red. If the
dimensions of the prism are 3 cm by 4 cm by 6 cm, how many of the cubes have exactly two sides
painted red?
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2) In right triangle AMC (see diagram) triangles ANP and
PLC are similar. MNPL is a square. Segment MC has
length 6 units and segment LC has length 4 units. What is
the area of triangle ANP?
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3) The points of an isosceles triangle are A=(2,3),
B=(3,1), and C=(1,1). If you rotate the triangle 180
degrees about the origin and then reflect the triangle
across the x-axis, what are the new coordinates for
A, B, and C?
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4) A dart board has a bull's-eye surrounded by 5 rings. The bull's-eye and the second and fourth rings are shaded (see diagram). If the bull's-eye has a radius of 2 cm, and each ring has a width of 2 cm, what is the area of all the shaded regions combined? Express your answer in terms of 
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5) When Andreyev wants to finish building the frame of the
front of his club house he notices that things aren't quite right.
The right post has a bit of a lean inwards and that messes with
the top beam. What is the angle between the left post and the
top beam? See diagram.