Whatcom County Math Championship – 2016 Geometry – 4th Grade 1. When Anya started reading, she looked at the clock and it read 6:45. When she stopped reading, the clock read 8:15. How many total degrees had the minute hand traveled? 2. A triangle has an area of 180 cm2 and a base of 45 cm. What is the height of the triangle? 3. How many triangles of all sizes are there in this picture:

4. Angelica made a staircase of three steps with 26 toothpicks, as shown below. How many toothpicks will she need to make a staircase of five steps?

5. A rectangle is made of two squares joined by one side. If the area of one of the squares is 64, what is the perimeter of the rectangle? 6. If you draw the diagonals of a square, they intersect at one point; if you do the same for a regular pentagon, they intersect at five points (as shown below). If you do the same for a regular hexagon, how many intersections will there be?

7. What fraction of the largest square is shaded? Give your answer as a fraction in lowest terms.

8. If a square of paper is folded in half to form a rectangle, and that rectangle has a perimeter of 24 cm, what is the area of the original square? 9. The floor of a square room is tiled with square tiles. If the room measured 5 x 5, then there would be 9 tiles along the two diagonals of the room. If there are 81 tiles along both diagonals, how many total tiles are there on the floor?

10. Annie arranges coins on a table in the figures below; after she’s made the figure, she draws a circle around it. If the coins each have an area of 12.56 cm2, what is the area of the circle she draws around figure 5? Round your answer to the nearest hundredth and use 3.14 for pi.

figure 1

figure 2

Whatcom County Math Championship – 2016 Geometry – 5th Grade 1. Angelica made a staircase of three steps with 26 toothpicks, as shown below. How many toothpicks will she need to make a staircase of five steps?

2. A rectangle is made of two squares joined by one side. If the area of one of the squares is 64, what is the perimeter of the rectangle? 3. If you draw the diagonals of a square, they intersect at one point; if you do the same for a regular pentagon, they intersect at five points (as shown below). If you do the same for a regular hexagon, how many intersections will there be?

4. What fraction of the largest square is shaded? Give your answer as a fraction in lowest terms.

5. If a square of paper is folded in half to form a rectangle, and that rectangle has a perimeter of 24 cm, what is the area of the original square? 6. The floor of a square room is tiled with square tiles. If the room measured 5 x 5, then there would be 9 tiles along the two diagonals of the room. If there are 81 tiles along both diagonals, how many total tiles are there on the floor?

7. Annie arranges coins on a table in the figures below; after she’s made the figure, she draws a circle around it. If the coins each have an area of 12.56 cm2, what is the area of the circle she draws around figure 5? Round your answer to the nearest hundredth and use 3.14 for pi.

figure 1

figure 2

8. How long is x in the figure below?

5

6 x

5

6 8

9. If the area of the larger regular hexagon is 180, what is the area of the smaller regular hexagon?

10. In the figure below, triangles AEF, AEB, EBD, BCD and ACF are all isosceles. What is the measure of ∠C?

A

B C

F  

E

D

Whatcom County Math Championship – 2016 Geometry – 6th Grade 1. What fraction of the largest square is shaded? Give your answer as a fraction in lowest terms.

2. If a square of paper is folded in half to form a rectangle, and that rectangle has a perimeter of 24 cm, what is the area of the original square? 3. The floor of a square room is tiled with square tiles. If the room measured 5 x 5, then there would be 9 tiles along the two diagonals of the room. If there are 81 tiles along both diagonals, how many total tiles are there on the floor?

4. Annie arranges coins on a table in the figures below; after she’s made the figure, she draws a circle around it. If the coins each have an area of 12.56 cm2, what is the area of the circle she draws around figure 5? Round your answer to the nearest hundredth and use 3.14 for pi.

figure 1

figure 2

5. How long is x in the figure below?

5

6 x

5

6 8

6. If the area of the larger regular hexagon is 180, what is the area of the smaller regular hexagon?

7. In the figure below, triangles AEF, AEB, EBD, BCD and ACF are all isosceles. What is the measure of ∠C?

A

B C

F

E

D

8. The line that goes through the points (–3, 2) and (5, –2) crosses the x – and y – axes at the points A and B. What is the area of the triangle formed by A, B and the origin? 9. A rectangle is made of two squares joined by one side. If the area of the rectangle is equal to the perimeter of the rectangle, what is that area? 10. A cube has a volume of 216 m2. What is the surface area, in square meters, of a cube that has side lengths 3 times the lengths of the original cube?  

Whatcom County Math Championship – 2016 Geometry – 7th + 8th Grade 1. Annie arranges coins on a table in the figures below; after she’s made the figure, she draws a circle around it. If the coins each have an area of 12.56 cm2, what is the area of the circle she draws around figure 5? Round your answer to the nearest hundredth and use 3.14 for pi.

figure 1

figure 2

2. How long is x in the figure below?

5

6 x

5

6 8

3. If the area of the larger regular hexagon is 180, what is the area of the smaller regular hexagon?

4. In the figure below, triangles AEF, AEB, EBD, BCD and ACF are all isosceles. What is the measure of ∠C?

A

B C

F

E

D

5. The line that goes through the points (–3, 2) and (5, –2) crosses the x – and y – axes at the points A and B. What is the area of the triangle formed by A, B and the origin? 6. A rectangle is made of two squares joined by one side. If the area of the rectangle is equal to the perimeter of the rectangle, what is that area? 7. A cube has a volume of 216 m2. What is the surface area, in square meters, of a cube that has side lengths 3 times the lengths of the original cube? 8. If the area of the square is 36, what is the area of the region marked with an *? Round your answer to the nearest hundredth.

*

9. In a 30-60-90 triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two pieces. If the smaller piece is length 1, how long is the larger piece? 10. In the figure below, two circles of radius 1 and 3 are tangent to each other and to the triangle surrounding them. What is the area of the triangle? (note: figure is not to scale) Round your answer to the nearest hundredth.

1

3