Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 7 Geometry
Problem
1) 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?
2) The circle shown has center point P and radius 5 units. What is the area of the shaded portion of the circle? Give your answer as an exact answer or round to the nearest hundredth. You may use the approximation = 3.142
3) The radius of all three semicircles is 1 unit. The height of the unshaded triangle is 3 units. What is the area of the shaded trapezoidal portion of the figure?

Problem
4) The coordinates of three of the vertices of a rhombus located in the first quadrant are: (2,5), (4,7) and (1,8). What are the coordinates of the fourth point? Use the coordinate grid to the right.
5) The figure shows a stained glass window design. The white triangles are congruent and equilateral and have side length 5 inches. The two triangles in the shaded region are isosceles with side lengths shown, and the central region is a rectangle. What is the area of the entire shaded region?