Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 8 Geometry
Problem
1) The area of the outside square is 64 square inches. Points A, B, C, and D are midpoints on their respective line segments. What is the area of the shaded circle? Give an exact answer in terms of
2) A garden is made up of three shaded equilateral triangles inside a circle as shown. The triangles have side length 10 feet. The parts of the circle that are not part of the garden are filled with white decorative rocks and are shown as the unshaded regions. What is the area covered by the white rocks? Give your answer as an exact answer OR rounded to the nearest tenth. You may use = 3.142

Problem
3) The surface area of a rectangular prism box is 288 square inches. Another box that has twice the width and twice the height has surface area 672 square inches. What is area of one side panel of the smaller box given by the product of its width and height?
4) Paula is playing around with sketches of a partially opened laptop. The top and the bottom of the laptop are both represented by parallelograms. If angle NPM is 45 degrees and angle MRS is 20 degrees, what is angle PMR?
5) If the rhombus in the figure is rotated clockwise around point P by 90 degrees, what will be the coordinates of the image of point R? Consider sketching the entire image rhombus to help you think.