Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 5 Geometry
Problem

1) The square shown is divided into 4 congruent rectangles. Each of them has perimeter 30 cm. What is the perimeter of the square?

2) The points A (4, 0), B (6, 4) and C (2, 6) are three vertices of a rhombus. The fourth vertex, D, also lies on this coordinate grid. What are the coordinates of D?

Problem

3) In the diagram, the length of the rectangle is 8 cm, the width is 6 cm. The area of isosceles triangle PDC is 4 cm2. The height of isosceles triangle PAB is 50% greater than the height of trapezoid ABCD. What is the area of isosceles trapezoid ABCD?

4) Quadrilateral ABCD has three congruent sides AB, AD, and DC. It has a right angle at A, an acute angle at D, and an obtuse angle at C. What must be true about the angle at D for all three conditions to hold?

5) Dee has 9 cubes. She wants to build a large cube that takes more than 9 cubes. What is the fewest number of cubes she would need to add to be able to build it?