Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2016 Grade 7 Geometry
Problem
Hint

1) Find the perimeter of the figure to the nearest centimeter. Each circular section has a radius of 13 cm.
  1. Note that the 2 quarter-circles on the bottom of the figure, when turned around, complete each of the 2 circles, therefore the perimeter (circumference) of the 2 circles is:

        C = _______ cm.

        2C = ________ cm.
  2. The additions are the 2 radii of the 2 quarter circles =
        ________ cm.
  3. Total = ____________ cm. (rounded)

2) The ratio of the angles of a triangle is 4:7:9. What is the measure of largest angle?
  1. The triangles angles are all multiples of ____ degrees.

  2. The largest angle is 9 of these = ______ degrees.

3) In rectangle ABCD, X is the midpoint of segment AB and Y is the midpoint of segment CD. The area of the shaded portion is 5.75 square inches. What is the area of the rectangle ABCD?
 The lines XC and BY cut the rectangle XBCY into 4 equal parts.
Therefore the area of ABCD is _____ sq. in.

Problem
Hint

4) A 110o section is taken from a circle with a radius of 4 inches and folded to create a cone by connecting the straight edges together. What is the radius of this cone? (Use 3.14 for pi)
(Round your answer to the nearest tenth of an inch)
  1. The circumference of the whole circle is _____ inches.

  2. The portion of the circumference that makes the cone is:
        ______________ inches.
  3. This is now the circumference of the base of the cone, so the radius of this cone is:
        r = ______________

5) In triangle XYZ, segment VW is parallel to XY. What is the measure of angle XVW?
  1. The measure of angle YXZ is _____ degrees.

  2. Triangles XYZ and VWX are similar triangles because their hypotenuses are parallel, so angle WVZ is equal to angle YXZ = _____ degrees.

  3. Angle XVW and angle WVZ add to 180 (a straight line) so angle XVW = ______ degrees.