Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2017 Grade 8 Geometry
Problem
1) What is the maximum number of 3 by 5 by 2 blocks that can be fit into a 16 by 23 by 10 box? The blocks must be stacked with the same orientation.

2) Triangle ABC has vertices at (2,3), (1, -2), and (-3, 1). The triangle gets reflected across the y-axis, rotated 90 degrees around the origin (counterclockwise ↶ ), then translated down three units. What are the coordinates of the resulting image's vertices?

3) What is the measure of angle CDB? Not drawn to scale

Problem
4) Give the length of side RS in radical form.
5) ABCD is a square. A, B, C, and D are the centers of their circles. The two smaller circles are congruent, and the two larger circles are congruent. DE = 4 inches and FA = 2 inches. Find the area of the shaded region. Express the answer to the nearest tenth.