Washington State Math Championship – 2015 Geometry – 4th Grade 1. In the figure below, the square is divided into strips of equal width. Two strips are shaded gray and one is shaded black. What fraction of the perimeter is shaded gray? Write your answer as a reduced fraction.

2. A triangle has angles of 36 and 73 degrees. What is the measure of the third angle? 3. The area of a square is 81. What is the perimeter? 4. How many lines of symmetry does a rectangle have? 5. If the four coordinates of a rectangle are (4, 7), (4, –2), (–3, 7) and (m, n), what is m + n? 6. How many degrees are in each angle of a regular pentagon? 7. How many squares and rectangles of all sizes are there in this picture?

8. Two rectangles measuring 5 cm x 6 cm and 8 cm x 9 cm overlap in the figure below. The grey shaded region has an area of 24 cm2. What is the area of the black region?

9. The area of a circle whose circumference is 18π is m π. What is the value of m? 10. The flag of Polygonia is a square in a rectangle; what is the shaded area?

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Washington State Math Championship – 2015 Geometry – 5th Grade 1. How many lines of symmetry does a rectangle have? 2. If the four coordinates of a rectangle are (4, 7), (4, –2), (–3, 7) and (m, n), what is m + n? 3. How many degrees are in each angle of a regular pentagon? 4. How many squares and rectangles of all sizes are there in this picture?

5. Two rectangles measuring 5 cm x 6 cm and 8 cm x 9 cm overlap in the figure below. The grey shaded region has an area of 24 cm2. What is the area of the black region?

6. The area of a circle whose circumference is 18π is m π. What is the value of m?

7. The flag of Polygonia is a square in a rectangle; what is the shaded area?

8 12 8. A square has an area of 144. If it is cut in half along a diagonal, what is the perimeter of one of the triangles that results? Round your answer to the nearest hundredth. 9. A square is surrounded by equilateral triangles. What is the measure of x, ∠ABC?

10. If a circle has a center at the point (6, 17) is tangent to another congruent circle at the point (8, 14), what are the coordinates of the center of the second circle?

Washington State Math Championship – 2015 Geometry – 6th Grade 1. How many squares and rectangles of all sizes are there in this picture?

2. Two rectangles measuring 5 cm x 6 cm and 8 cm x 9 cm overlap in the figure below. The grey shaded region has an area of 24 cm2. What is the area of the black region?

3. The area of a circle whose circumference is 18π is m π. What is the value of m? 4. The flag of Polygonia is a square in a rectangle; what is the shaded area?

8 12 5. A square has an area of 144. If it is cut in half along a diagonal, what is the perimeter of one of the triangles that results? Round your answer to the nearest hundredth.

6. A square is surrounded by equilateral triangles. What is the measure of x, ∠ABC?

7. If a circle has a center at the point (6, 17) is tangent to another congruent circle at the point (8, 14), what are the coordinates of the center of the second circle? 8. How many numbers in the set {1, 2, 3, …, 12} cannot be the degree measure of the exterior angle of a regular polygon? 9. What is the area between the x-axis, the y-axis, and the function y = 4 –| x – 2 | 10. ∠ABD = 15° and ΔABC is a right triangle. How long is segment AD? Round your answer to the nearest hundredth.

Washington State Math Championship – 2015 Geometry – 7th + 8th Grade 1. The flag of Polygonia is a square in a rectangle; what is the shaded area?

8 12 2. A square has an area of 144. If it is cut in half along a diagonal, what is the perimeter of one of the triangles that results? Round your answer to the nearest hundredth. 3. A square is surrounded by equilateral triangles. What is the measure of x, ∠ABC?

4. If a circle has a center at the point (6, 17) is tangent to another congruent circle at the point (8, 14), what are the coordinates of the center of the second circle? 5. How many numbers in the set {1, 2, 3, …, 12} cannot be the degree measure of the exterior angle of a regular polygon? 6. What is the area between the x-axis, the y-axis, and the function y = 4 –| x – 2 |

7. ∠ABD = 15° and ΔABC is a right triangle. How long is segment AD? Round your answer to the nearest hundredth.

8. If the four coordinates of a rectangle are (4, 6), (8, 4), (–2, –6) and (m, n), what is m + n? 9. What is the area of this regular pentagon? Round your answer to the nearest hundredth.

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10. In figure below, ABCD is a square with length 1. Corners A and C are folded in, resulting in hexagon BEFDGH, with segments EF and GH parallel. If that hexagon is equilateral, how long is one side of the hexagon? Round your answer to the nearest hundredth.   B

x

1

1

C

A 1

A

E

H

F

G

C

1 D

 

B

B

D

D