Geometry
Grade 4
1. What is the area of a square whose perimeter is twelve inches?
2. What is the measure of the third angle in a triangle whose other two angles have measures of 24
degrees and 45 degrees?
3. If the area of the following figure is 200 square units, and each of the squares have an equal area,
what is the perimeter of the figure?
4.
If the length of two sides on an isosceles triangle are 12cm and 8cm, what is the greatest possible
perimeter the triangle can have?
5. How many degrees are in each interior angle of a regular octagon?
6. How many of the shapes on the second line are congruent to the shape on the first line?
7. Equilateral triangles are placed on each side of a regular octagon such that the base of each triangle
is one of the sides of the octagon. If each side of the octagon is 4cm, what is the perimeter of the
new figure?
8. Two trees have their bases 24 meters apart from each other. The first tree is 48 meters tall and the
other tree is 58 meters tall. What is the shortest distance a bird could fly to go from the top of one
tree to the other?
Geometry
Grade 4
9. Suppose a cross-country athlete was preparing for the next meet by running laps around his
school's circular track. If the athlete needs to run 6 miles, and the radius of the track is 0.5 miles,
how many full laps will he need to run in order to reach his goal?
10. By drawing three straight lines, what is the greatest number of regions you can split the following
rectangle into?
Geometry
Grade 5
1. If the area of the following figure is 200 square units, and each of the squares have an equal area,
what is the perimeter of the figure?
2.
If the length of two sides on an isosceles triangle are 12cm and 8cm, what is the greatest possible
perimeter the triangle can have?
3. How many degrees are in each interior angle of a regular octagon?
4. How many of the shapes on the second line are congruent to the shape on the first line?
5. Equilateral triangles are placed on each side of a regular octagon such that the base of each triangle
is one of the sides of the octagon. If each side of the octagon is 4cm, what is the perimeter of the
new figure?
6. Two trees have their bases 24 meters apart from each other. The first tree is 48 meters tall and the
other tree is 58 meters tall. What is the shortest distance a bird could fly to go from the top of one
tree to the other?
7. Suppose a cross-country athlete was preparing for the next meet by running laps around his
school's circular track. If the athlete needs to run 6 miles, and the radius of the track is 0.5 miles,
how many full laps will he need to run in order to reach his goal?
Geometry
Grade 5
8. By drawing three straight lines, what is the greatest number of regions you can split the following
rectangle into?
9. Suppose a flower bed measures 21 feet by 21 feet, and there is a cement path with constant width
going around the flower bed. If the total area of the path is equal to 184 square feet, what is the
width of the path?
10. What is the area of the trapezoid shown below? Express your answer to the nearest integer.
8 cm
8 cm
6 cm
8 cm
Geometry
Grade 6
1. How many degrees are in each interior angle of a regular octagon?
2. How many of the shapes on the second line are congruent to the shape on the first line?
3. Equilateral triangles are placed on each side of a regular octagon such that the base of each triangle
is one of the sides of the octagon. If each side of the octagon is 4cm, what is the perimeter of the
new figure?
4. Two trees have their bases 24 meters apart from each other. The first tree is 48 meters tall and the
other tree is 58 meters tall. What is the shortest distance a bird could fly to go from the top of one
tree to the other?
5. Suppose a cross-country athlete was preparing for the next meet by running laps around his
school's circular track. If the athlete needs to run 6 miles, and the radius of the track is 0.5 miles,
how many full laps will he need to run in order to reach his goal?
6. By drawing three straight lines, what is the greatest number of regions you can split the following
rectangle into?
Geometry
Grade 6
7. Suppose a flower bed measures 21 feet by 21 feet, and there is a cement path with constant width
going around the flower bed. If the total area of the path is equal to 184 square feet, what is the
width of the path?
8.
What is the area of the trapezoid shown below? Express your answer to the nearest integer.
8 cm
8 cm
6 cm
8 cm
9. How many of the following symbols have rotational symmetry?
          
           
10. Four vertices of a square are at points with the coordinates (2, 4), (-3, 5), (1,0), and (a, b). What
are the coordinates of the vertex denoted by (a, b)? Express your answer in the form: (a, b).
Geometry
Grade 7
1. Equilateral triangles are placed on each side of a regular octagon such that the base of each
triangle is one of the sides of the octagon. If each side of the octagon is 4cm, what is the
perimeter of the new figure?
2. Two trees have their bases 24 meters apart from each other. The first tree is 48 meters tall and the
other tree is 58 meters tall. What is the shortest distance a bird could fly to go from the top of one
tree to the other?
3. Suppose a cross-country athlete was preparing for the next meet by running laps around his
school's circular track. If the athlete needs to run 6 miles, and the radius of the track is 0.5 miles,
how many full laps will he need to run in order to reach his goal?
4. By drawing three straight lines, what is the greatest number of regions you can split the following
rectangle into?
5. Suppose a flower bed measures 21 feet by 21 feet, and there is a cement path with constant width
going around the flower bed. If the total area of the path is equal to 184 square feet, what is the
width of the path?
6.
What is the area of the trapezoid shown below? Express your answer to the nearest integer.
8 cm
8 cm
6 cm
8 cm
Geometry
Grade 7
7. How many of the following symbols have rotational symmetry?
          
           
8. Four vertices of a square are at points with the coordinates (2, 4), (-3, 5), (1,0), and (a, b). What
are the coordinates of the vertex denoted by (a, b)? Express your answer in the form: (a, b).
9. Suppose a square is inscribed inside of a circle, and then a circle is inscribed inside of that square.
How many times larger is the area of the outer circle than the inner circle?
10. If the radius of the circle below is 6 units and angle AOB has a measure of 90 degrees, to the
nearest tenth of a unit, what is the area of the smaller sector?
Geometry
Grade 8
1. Suppose a cross-country athlete was preparing for the next meet by running laps around his
school's circular track. If the athlete needs to run 6 miles, and the radius of the track is 0.5 miles,
how many full laps will he need to run in order to reach his goal?
2. By drawing three straight lines, what is the greatest number of regions you can split the following
rectangle into?
3. Suppose a flower bed measures 21 feet by 21 feet, and there is a cement path with constant width
going around the flower bed. If the total area of the path is equal to 184 square feet, what is the
width of the path?
4.
What is the area of the trapezoid shown below? Express your answer to the nearest integer.
8 cm
8 cm
6 cm
8 cm
5. How many of the following symbols have rotational symmetry?
          
           
Geometry
Grade 8
6. Four vertices of a square are at points with the coordinates (2, 4), (-3, 5), (1,0), and (a, b). What
are the coordinates of the vertex denoted by (a, b)? Express your answer in the form: (a, b).
7. Suppose a square is inscribed inside of a circle, and then a circle is inscribed inside of that square.
How many times larger is the area of the outer circle than the inner circle?
8. If the radius of the circle below is 6 units and angle AOB has a measure of 90 degrees, to the
nearest tenth of a unit, what is the area of the smaller sector?
9.
What is the smaller of the two angles formed by the hour and minute hand at 8:10?
10. If a spherical toy ball is circumscribed around a cube, and the radius of the sphere is 3 inches, how
much space within the sphere, to the nearest hundredth of a cubic inch, is not occupied by the
cube?