Geometry
5th Grade
Instructions: Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely.
You do not need to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If
3
your answer is a fraction like
, bubble in 316. For decimal answers like 3.14, bubble in 314.
16
1. 2 points: If the perimeter of a rectangle is 24 inches and the length of the rectangle is 3 inches,
what is the width of the rectangle in inches?
2. 2 points: A 26 foot long ladder is leaning up against a house with its base 10 feet away from the
house on the ground. If the side of the house is perfectly vertical, how far up the house would you
be if you climbed to the top of the ladder? Express your answer in feet.
3. 2 points: A pie baker likes to make pies that are neatly sliced into pieces that each have an area
of π square inches. How many slices would he have to cut his 14-inch diameter pie into in order
to continue his tradition?
4. 3 points: What is the area of the unshaded region in the following figure?
8
2
8
6
3
2
13
5. 3 points: If the degree measures of the interior angles of a pentagon are x+2, 3x-10, 2x+20, x-20,
and 2x+8, what is the degree measure of the largest angle?
6. 3 points: How many unique diagonals can be drawn in a regular decagon?
7. 3 points: A group of toy makers want to wrap the world's biggest toy block with wrapping paper.
The block has dimensions of eight feet by six feet by twelve feet. How much wrapping paper, in
square feet, will they need in order to wrap the entire toy block? Assume there is no overlap in
wrapping paper.
www.blainesd.org/mathchamps/
Geometry
5th Grade
8. 4 points: In a drawing of her snowman creation in the backyard, Elsie drew three circles of radii
8, 6, and 4 as seen below. If she wanted to draw a line from the ear, located at the farthest right
point of the top circle to the farthest left point on the bottom circle, how long of a line would she
be drawing? Express your answer to the nearest unit.
9. 4 points: The owners of a neighborhood pool wanted to build a safe rubber walkway around the
pool that is one foot wide. If the pool is 30 feet by 20 feet, what will the area, in square feet, of
the rubber walkway be?
10. 4 points: Which of the following diagrams cannot be folded into a cube?
a)
b)
d)
e)
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c)
Geometry
6th Grade
Instructions: Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely.
You do not need to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If
3
your answer is a fraction like
, bubble in 316. For decimal answers like 3.14, bubble in 314.
16
1. 2 points: What is the area of the unshaded region in the following figure?
8
2
8
6
3
2
13
2. 2 points: If the degree measures of the interior angles of a pentagon are x+2, 3x-10, 2x+20, x-20,
and 2x+8, what is the degree measure of the largest angle?
3. 2 points: How many unique diagonals can be drawn in a regular decagon?
4. 3 points: A group of toy makers want to wrap the world's biggest toy block with wrapping paper.
The block has dimensions of eight feet by six feet by twelve feet. How much wrapping paper, in
square feet, will they need in order to wrap the entire toy block? Assume there is no overlap in
wrapping paper.
5. 3 points: In a drawing of her snowman creation in the backyard, Elsie drew three circles of radii
8, 6, and 4 as seen below. If she wanted to draw a line from the ear, located at the farthest right
point of the top circle to the farthest left point on the bottom circle, how long of a line would she
be drawing? Express your answer to the nearest unit.
www.blainesd.org/mathchamps/
Geometry
6th Grade
6. 3 points: The owners of a neighborhood pool wanted to build a safe rubber walkway around the
pool that is one foot wide. If the pool is 30 feet by 20 feet, what will the area, in square feet, of
the rubber walkway be?
7. 3 points: Which of the following diagrams cannot be folded into a cube?
a)
b)
d)
e)
c)
8. 4 points: If a triangle must have a non-zero area, how many integral lengths are possible for the
third side of a triangle whose other two sides have lengths of 3 and 11?
9. 4 points: Mrs. Bermuda gives you two mystery triangles and tells you the following information
about them: Triangle A has one side length of six units and an area of 48 square units. Triangle B
is similar to triangle A, and has an area of 12 square units. What is the length of the
corresponding side of triangle B?
10. 4 points: Suppose a swimming pool is 12.5 meters in length, 25 meters wide, and three meters
deep. If one tank of water will fill one cubic meter, how many tanks of water would be needed to
fill the pool 80% full?
www.blainesd.org/mathchamps/
Geometry
7th Grade
Instructions: Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely.
You do not need to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If
3
your answer is a fraction like
, bubble in 316. For decimal answers like 3.14, bubble in 314.
16
1. 2 points: A group of toy makers who happen to be Seahawks fans want to wrap the world's
biggest toy block with wrapping paper. The block has dimensions of eight feet by six feet by
twelve feet. How much wrapping paper, in square feet, will they need in order to wrap the entire
toy block? Assume there is no overlap in wrapping paper.
2. 2 points: In a drawing of her snowman creation in the backyard, Elsie drew three circles of radii
8, 6, and 4 as seen below. If she wanted to draw a line from the ear, located at the farthest right
point of the top circle to the farthest left point on the bottom circle, how long of a line would she
be drawing? Express your answer to the nearest unit.
3. 2 points: The owners of a neighborhood pool wanted to build a safe rubber walkway around the
pool that is one foot wide. If the pool is 30 feet by 20 feet, what will the area, in square feet, of
the rubber walkway be?
4. 3 points: Which of the following diagrams cannot be folded into a cube?
a)
b)
d)
e)
www.blainesd.org/mathchamps/
c)
Geometry
7th Grade
5. 3 points: If a triangle must have a non-zero area, how many integral lengths are possible for the
third side of a triangle whose other two sides have lengths of 3 and 11?
6. 3 points: Mrs. Bermuda gives you two mystery triangles and tells you the following information
about them: Triangle A has one side length of six units and an area of 48 square units. Triangle B
is similar to triangle A, and has an area of 12 square units. What is the length of the
corresponding side of triangle B?
7. 3 points: Suppose a swimming pool is 12.5 meters in length, 25 meters wide, and three meters
deep. If one tank of water will fill one cubic meter, how many tanks of water would be needed to
fill the pool 80% full?
8. 4 points: In the following diagram, if the measure of angle TLK is 58 degrees, what is the degree
measure of angle LEV? Assume that line KP is parallel to line CV.
9. 4 points: If an airplane is taking off from the ground at a constant rate of 120 mph and at a
constant angle of 30 degrees with the ground, how many miles above the ground will the plane be
after five minutes?
10. 4 points: In the figure below, how many triangles of any size are there?
www.blainesd.org/mathchamps/
Geometry
8th Grade
Instructions: Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely.
You do not need to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If
3
your answer is a fraction like
, bubble in 316. For decimal answers like 3.14, bubble in 314.
16
1. 2 points: Which of the following diagrams cannot be folded into a cube?
a)
b)
d)
e)
c)
2. 2 points: If a triangle must have a non-zero area, how many integral lengths are possible for the
third side of a triangle whose other two sides have lengths of 3 and 11?
3. 2 points: Mrs. Bermuda gives you two mystery triangles and tells you the following information
about them: Triangle A has one side length of six units and an area of 48 square units. Triangle B
is similar to triangle A, and has an area of 12 square units. What is the length of the
corresponding side of triangle B?
4. 3 points: Suppose a swimming pool is 12.5 meters in length, 25 meters wide, and three meters
deep. If one tank of water will fill one cubic meter, how many tanks of water would be needed to
fill the pool 80% full?
5. 3 points: In the following diagram, if the measure of angle TLK is 58 degrees, what is the degree
measure of angle LEV? Assume that line KP is parallel to line CV.
www.blainesd.org/mathchamps/
Geometry
8th Grade
6. 3 points: If an airplane is taking off from the ground at a constant rate of 120 mph and at a
constant angle of 30 degrees with the ground, how many miles above the ground will the plane be
after five minutes?
7. 3 points: In the figure below, how many triangles of any size are there?
8. 4 points: What is the perimeter of a triangle whose vertices are at the points with coordinates (2,
4), (4, 10), and (-2, 3)? Express your answer to the nearest tenth of a unit.
9. 4 points: A cone-shaped water cup is leaking from the bottom at a rate of 2.5 percent of its
original volume per second. In how many seconds will the cup be filled to half its original height?
10. 4 points: In terms of volume, if the base of a right circular cylinder must have an area of 20π,
what is the largest such cylinder that can fit inside of a sphere of radius 6? Express your answer
to the nearest cubic unit.
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