Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 6 Geometry
Problem
1) What is the area of the shaded portion of the circle of radius 5 units? Point P is the center of the circle. You may give an exact answer or an approximation to the nearest tenth using the approximation = 3.14.
2) The formula for the area of a triangle is often gotten by looking at a related parallelogram. For triangle ABC shown on the coordinate grid what are the coordinates of the vertices of a parallelogram in the first quadrant that has twice the area of the triangle and contains the triangle?

Problem
3) The surface area of a rectangular prism box is 288 square inches. Another rectangular prism box has double each dimension so twice the length, twice the width and twice the height or the first box. What is its surface area?

4) The rhombus in quadrant I is reflected across the x-axis. Sketch and label its coordinates on the coordinate axes provided on the answer sheet.
5) Two congruent isosceles triangles are joined together along a side to create a kite as shown. The perimeter of one of the triangles is 30 units. The lengths of the sides of the triangle are all whole numbers. What is the length of the longest side of the triangle if the perimeter of the kite is as long as possible?