Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 7 Geometry
Problem
1) How many squares are in this figure?

2) Jacob wants to measure the height of his house using shadows. Jacob is 5 feet 10 inches tall and casts a shadow that is 2 feet 6 inches long. His house casts a shadow that is 9 feet 6 inches long. What is the height of Jacob's house?

3) A container used for gardening measures 14 in across and 3 ft wide, capped with a half circle at each end as shown. It is 3/4 ft deep. What is the volume of soil needed to fill it?
(Express your answer to the nearest tenth of a cubic feet.)

Problem
4) A rectangular wooden block measuring 8 cm by 14 cm by 18 cm is painted green all around and then cut into 2 cm cubes. What is the ratio of cubes that are painted on one or more sides to cubes with none of the faces painted? Expressed your answer in the lowest term.

5) XYZ is an equilateral triangle, 12 units to a side. X, Y, and Z are also the center points of three equal circles that intersect without overlapping. In the figure below, what is the area of the shaded section to the nearest tenth of a unit?
(Use 3.14 for pi)