Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 5 Geometry
Problem
1) Sarah is making tickets for the school dance. What is the maximum number of 1 1/2 x 2 1/2 inch tickets she can cut from a 8 1/2 x 11 inch sheet of card stock paper?

2) An isosceles trapezoid has a line of symmetry. Three of the vertices of the isosceles trapezoid are (1, 6 ), (3, 2), and (7, 2) as shown. The fourth vertex has whole number coordinates. What are the coordinates of the fourth vertex?
3) The first figure is a square with side length 3 units. The second figure is obtained from the first by replacing each middle third of a side with three sides of a square. The third figure is obtained from the second by replacing each middle third of a side with three sides of a square. What is the area of the third figure? The third figure is not accurately drawn, it is there to help you visualize.
Express your answer as a mixed number.

Problem

4) At twelve noon the angle between the hour and minute hands on an analogue clock is 0 degrees. What is the angle between the hands on the clock at 12:30 pm (30 minutes later)?

5) To find the area of parallelogram ABCD, Drew draws the perpendicular segments DS and BT. He does some measuring. To the nearest tenth of a centimeter BC = 7 cm, CT = 6.7 cm, BS = 5 cm, and DS = 2.1 cm. If he has enough information to compute the area of parallelogram ABCD, then compute the area to the nearest tenth of a square centimeter. If he needs to make more measurements, list the segments he needs to measure.