Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 8 Measurement

Problem
1) A rectangle has length 4 inches and width 3 inches. An isosceles triangle is formed by cutting the rectangle along its diagonal and joining the two triangles formed along the long side of the rectangle, see diagram. What is the perimeter of the new triangle?
2) What is the area of a regular octagon with side length 1 cm (see picture)? You may leave square roots in your answer but simplify as much as possible or round to the nearest thousandth.

Problem
3) 800 liters of water are poured into a circular inflatable swimming pool. If the diameter of the pool is 160 centimeter how deep is the water to the nearest centimeters? 1 liter is the same as 1000 cubic centimeters of water.
You may use = 3.14

4) An odd little man lives by himself in an isolated house that no one ever visits. He loves money. He has covered one 120 square foot wall with $10 bills with no gaps and no overlaps. He decides instead he wants to enjoy the sight of the $10 bills in many rooms and will make a continuous strip of them along the hallways and in and out of rooms. He can place the $10 bills with no gaps or overlaps so that the strip is 1/2 foot wide or 5/24 foot wide. How much longer would the 5/24 foot wide strip be than the 1/2 foot wide strip?

5) A wooden shipping crate is measured for shipping. Its length is 8 feet and its girth (going completely once around in the direction perpendicular to the length) is 24 feet. The surface area of the lid of the crate is 40 square feet. The dimensions are whole numbers of feet. What is the volume of the crate in cubic feet?