Geometry Tutor Worksheet 11 Perimeter
Geometry Tutor Worksheet 11 Perimeter
1 © MathTutorDVD.com
Geometry Tutor - Worksheet 11 – Perimeter 1. What is the perimeter of the square?
2. What is the perimeter of the pentagon?
3. What is the perimeter of the figure below? All angles in the figure are right angles.
2 © MathTutorDVD.com
4. What is the perimeter of the triangle?
5. What is the perimeter of the rectangle?
6. What is the perimeter of the figure below? All angles in the figure are right angles.
3 © MathTutorDVD.com
7. What is the perimeter of the figure below? All angles in the figure are right angles.
8. What is the perimeter of the figure below? All angles in the figure are right angles.
9. What is the perimeter of the figure below? All angles in the figure are right angles.
4 © MathTutorDVD.com
10. What is the perimeter of the figure below? All angles in the figure are right angles.
11. What is the perimeter of the figure below? All angles in the figure are right angles.
12. What is the perimeter of the figure below? All angles in the figure are right angles.
5 © MathTutorDVD.com
13. A race is being organized that follows the path in the figure below. What is the length of the race? All angles in the figure are right angles.
14. What is the perimeter of the figure below? All angles in the figure are right angles.
15. What is the perimeter of the figure below? All angles in the figure are right angles.
6 © MathTutorDVD.com
16. What is the perimeter of the star below?
17. What is the perimeter of the irregular polygon below?
18. A community fundraising group has organized a bicycle race that follows the route in the figure below. How long is the race?
7 © MathTutorDVD.com
19. The courtyard of a new office building is in the shape of the irregular polygon below. The architectural drawings show a special border for the courtyard. How much border does the builder need to buy?
20. What is the perimeter of the hexagon below?
21. What is the perimeter of the irregular polygon below?
8 © MathTutorDVD.com
Answers - Geometry Tutor - Worksheet 11 – Perimeter 1. What is the perimeter of the square?
The formula for the perimeter of a square is 𝑃 = 4𝑠 where 𝑃 is the perimeter and 1
𝑠 is the length of one side. Thus, 𝑃 = 4 (2 ) = 10. The unit is cm. 2 Answer: 10 cm
2. What is the perimeter of the pentagon?
The markings show that the pentagon is a regular pentagon, which means all sides have an equal length. The formula for the perimeter of a regular pentagon is 𝑃 = 5𝑠 where 𝑃 is the perimeter and 𝑠 is the length of one side. Thus, 𝑃 = 5(3) = 15. The unit is m. Answer: 15 m
3. What is the perimeter of the figure below? All angles in the figure are right angles.
9 © MathTutorDVD.com
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 2 + 3 + 2 + 3 + 6 + 6 + 6 = 30. The unit is dm. Answer: 30 dm
4. What is the perimeter of the triangle?
The figure is a triangle. To find the perimeter add the lengths of the three sides: 2√7 + 3√7 + 4√7 = 9√7. The unit is m. 10 © MathTutorDVD.com
Answer: 9√7 m
5. What is the perimeter of the rectangle?
The figure is a rectangle. The formula for the perimeter of a rectangle is 𝑃 = 2𝑙 + 2𝑤 where 𝑃 is the perimeter, 𝑙 is the length, and 𝑤 is the width, so 𝑃 = 2(9) + 2(3) = 24; the unit is ft. Answer: 24 ft.
6. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
11 © MathTutorDVD.com
Add all of the lengths: 6 + 2 + 9 + 9 + 15 + 11 = 52. The unit is km. Answer: 52 km
7. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 2.5 + 1.5 + 1 + 2 + 5 + 1 + 1.5 + 2.5 = 17. The unit is dm. 12 © MathTutorDVD.com
Answer: 17 dm
8. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 5 + 7 + 13 + 1 + 8 + 6 = 40. The unit is mm. Answer: 40 mm
9. What is the perimeter of the figure below? All angles in the figure are right angles.
13 © MathTutorDVD.com
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 25 + 6 + 7 + 16 + 18 + 22 = 94. The unit is mm. Answer: 94 mm
10. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. However, the units in the figure are not all the same. Change the 14 © MathTutorDVD.com
centimeters to millimeters. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 20 + 55 + 60 + 45 + 80 + 100 = 360. The unit is mm. This answer can also be expressed in centimeters. Answer: 360 mm or 36 cm
11. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
15 © MathTutorDVD.com
Add all of the lengths: 2.5 + 1.2 + 1 + 0.8 + 1 + 1.5 + 0.5 + 0.5 = 9. The unit is m. Answer: 9 m
12. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 125 + 50 + 25 + 40 + 100 + 90 = 430. The unit is cm. Answer: 430 cm
13. A race is being organized that follows the path in the figure below. What is the length of the race? All angles in the figure are right angles.
16 © MathTutorDVD.com
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 1.2 + 0.8 + 0.2 + 0.2 + 1 + 1 = 4.4. The unit is km. Answer: 4.4 km
14. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
17 © MathTutorDVD.com
Add all of the lengths: 12 + 9 + 5 + 6 + 7 + 3 = 42. The unit is cm. Answer: 42 cm
15. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 6 + 9 + 14 + 6 + 20 + 15 = 70. The unit is m. Answer: 70 m 18 © MathTutorDVD.com
16. What is the perimeter of the star below?
The markings on the figure show that all sides have the same length. The figure has 10 sides, so the perimeter can be calculated using the formula 𝑃 = 10𝑠 where 𝑃 is the perimeter and 𝑠 is the length of each side. Thus, 𝑃 = 10(8) = 80. The unit is mm. Answer: 80 mm
17. What is the perimeter of the irregular polygon below?
The figure is an irregular polygon so there is no formula for calculating the perimeter. Add the lengths of all of the sides. 𝑃 = 3 + 2 + 1 + 6 + 5 + 4 = 21 The unit is hm. Answer: 21 hm 19 © MathTutorDVD.com
18. A community fundraising group has organized a bicycle race that follows the route in the figure below. How long is the race?
The figure is an irregular polygon so there is no formula for calculating the perimeter. Add the lengths of all of the sides. 𝑃 = 10 + 5 + 4 + 2 + 2 + 3 + 3 + 2 + 6 = 37 The unit is km. Answer: 37 km
19. The courtyard of a new office building is in the shape of the irregular polygon below. The architectural drawings show a special border for the courtyard. How much border does the builder need to buy?
The figure is an irregular polygon so there is no formula for calculating the perimeter. However, the figure shows horizontal symmetry which means the sides on the left have the same lengths as the sides on the right. Add the lengths of all of the sides. 20 © MathTutorDVD.com
𝑃 = 8 + 4 + 13 + 5 + 13 + 4 + 8 = 55 The unit is m. Answer: 55 m
20. What is the perimeter of the hexagon below?
The figure is an irregular polygon so there is no formula for calculating the perimeter. However, the figure shows vertical and horizontal symmetry which means sides are marked as having the same lengths as other sides. Add the lengths of all of the sides. 𝑃 = 4 + 2 + 2 + 4 + 2 + 2 = 16 The unit is cm. Answer: 16 cm
21. What is the perimeter of the irregular polygon below?
21 © MathTutorDVD.com
The markings on the figure show that all sides have the same length. The figure has 14 sides, so the perimeter can be calculated using the formula 𝑃 = 14𝑠 where 𝑃 is the perimeter and 𝑠 is the length of each side. Thus, 𝑃 = 14(3) = 42. The unit is cm. Answer: 42 cm
22 © MathTutorDVD.com
1 © MathTutorDVD.com
Geometry Tutor - Worksheet 11 – Perimeter 1. What is the perimeter of the square?
2. What is the perimeter of the pentagon?
3. What is the perimeter of the figure below? All angles in the figure are right angles.
2 © MathTutorDVD.com
4. What is the perimeter of the triangle?
5. What is the perimeter of the rectangle?
6. What is the perimeter of the figure below? All angles in the figure are right angles.
3 © MathTutorDVD.com
7. What is the perimeter of the figure below? All angles in the figure are right angles.
8. What is the perimeter of the figure below? All angles in the figure are right angles.
9. What is the perimeter of the figure below? All angles in the figure are right angles.
4 © MathTutorDVD.com
10. What is the perimeter of the figure below? All angles in the figure are right angles.
11. What is the perimeter of the figure below? All angles in the figure are right angles.
12. What is the perimeter of the figure below? All angles in the figure are right angles.
5 © MathTutorDVD.com
13. A race is being organized that follows the path in the figure below. What is the length of the race? All angles in the figure are right angles.
14. What is the perimeter of the figure below? All angles in the figure are right angles.
15. What is the perimeter of the figure below? All angles in the figure are right angles.
6 © MathTutorDVD.com
16. What is the perimeter of the star below?
17. What is the perimeter of the irregular polygon below?
18. A community fundraising group has organized a bicycle race that follows the route in the figure below. How long is the race?
7 © MathTutorDVD.com
19. The courtyard of a new office building is in the shape of the irregular polygon below. The architectural drawings show a special border for the courtyard. How much border does the builder need to buy?
20. What is the perimeter of the hexagon below?
21. What is the perimeter of the irregular polygon below?
8 © MathTutorDVD.com
Answers - Geometry Tutor - Worksheet 11 – Perimeter 1. What is the perimeter of the square?
The formula for the perimeter of a square is 𝑃 = 4𝑠 where 𝑃 is the perimeter and 1
𝑠 is the length of one side. Thus, 𝑃 = 4 (2 ) = 10. The unit is cm. 2 Answer: 10 cm
2. What is the perimeter of the pentagon?
The markings show that the pentagon is a regular pentagon, which means all sides have an equal length. The formula for the perimeter of a regular pentagon is 𝑃 = 5𝑠 where 𝑃 is the perimeter and 𝑠 is the length of one side. Thus, 𝑃 = 5(3) = 15. The unit is m. Answer: 15 m
3. What is the perimeter of the figure below? All angles in the figure are right angles.
9 © MathTutorDVD.com
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 2 + 3 + 2 + 3 + 6 + 6 + 6 = 30. The unit is dm. Answer: 30 dm
4. What is the perimeter of the triangle?
The figure is a triangle. To find the perimeter add the lengths of the three sides: 2√7 + 3√7 + 4√7 = 9√7. The unit is m. 10 © MathTutorDVD.com
Answer: 9√7 m
5. What is the perimeter of the rectangle?
The figure is a rectangle. The formula for the perimeter of a rectangle is 𝑃 = 2𝑙 + 2𝑤 where 𝑃 is the perimeter, 𝑙 is the length, and 𝑤 is the width, so 𝑃 = 2(9) + 2(3) = 24; the unit is ft. Answer: 24 ft.
6. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
11 © MathTutorDVD.com
Add all of the lengths: 6 + 2 + 9 + 9 + 15 + 11 = 52. The unit is km. Answer: 52 km
7. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 2.5 + 1.5 + 1 + 2 + 5 + 1 + 1.5 + 2.5 = 17. The unit is dm. 12 © MathTutorDVD.com
Answer: 17 dm
8. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 5 + 7 + 13 + 1 + 8 + 6 = 40. The unit is mm. Answer: 40 mm
9. What is the perimeter of the figure below? All angles in the figure are right angles.
13 © MathTutorDVD.com
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 25 + 6 + 7 + 16 + 18 + 22 = 94. The unit is mm. Answer: 94 mm
10. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. However, the units in the figure are not all the same. Change the 14 © MathTutorDVD.com
centimeters to millimeters. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 20 + 55 + 60 + 45 + 80 + 100 = 360. The unit is mm. This answer can also be expressed in centimeters. Answer: 360 mm or 36 cm
11. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
15 © MathTutorDVD.com
Add all of the lengths: 2.5 + 1.2 + 1 + 0.8 + 1 + 1.5 + 0.5 + 0.5 = 9. The unit is m. Answer: 9 m
12. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 125 + 50 + 25 + 40 + 100 + 90 = 430. The unit is cm. Answer: 430 cm
13. A race is being organized that follows the path in the figure below. What is the length of the race? All angles in the figure are right angles.
16 © MathTutorDVD.com
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 1.2 + 0.8 + 0.2 + 0.2 + 1 + 1 = 4.4. The unit is km. Answer: 4.4 km
14. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
17 © MathTutorDVD.com
Add all of the lengths: 12 + 9 + 5 + 6 + 7 + 3 = 42. The unit is cm. Answer: 42 cm
15. What is the perimeter of the figure below? All angles in the figure are right angles.
Since all angles are right angles, opposite sides of the figure have the same length as in rectangles. This allows us to identify the lengths of the unlabeled sides as
Add all of the lengths: 6 + 9 + 14 + 6 + 20 + 15 = 70. The unit is m. Answer: 70 m 18 © MathTutorDVD.com
16. What is the perimeter of the star below?
The markings on the figure show that all sides have the same length. The figure has 10 sides, so the perimeter can be calculated using the formula 𝑃 = 10𝑠 where 𝑃 is the perimeter and 𝑠 is the length of each side. Thus, 𝑃 = 10(8) = 80. The unit is mm. Answer: 80 mm
17. What is the perimeter of the irregular polygon below?
The figure is an irregular polygon so there is no formula for calculating the perimeter. Add the lengths of all of the sides. 𝑃 = 3 + 2 + 1 + 6 + 5 + 4 = 21 The unit is hm. Answer: 21 hm 19 © MathTutorDVD.com
18. A community fundraising group has organized a bicycle race that follows the route in the figure below. How long is the race?
The figure is an irregular polygon so there is no formula for calculating the perimeter. Add the lengths of all of the sides. 𝑃 = 10 + 5 + 4 + 2 + 2 + 3 + 3 + 2 + 6 = 37 The unit is km. Answer: 37 km
19. The courtyard of a new office building is in the shape of the irregular polygon below. The architectural drawings show a special border for the courtyard. How much border does the builder need to buy?
The figure is an irregular polygon so there is no formula for calculating the perimeter. However, the figure shows horizontal symmetry which means the sides on the left have the same lengths as the sides on the right. Add the lengths of all of the sides. 20 © MathTutorDVD.com
𝑃 = 8 + 4 + 13 + 5 + 13 + 4 + 8 = 55 The unit is m. Answer: 55 m
20. What is the perimeter of the hexagon below?
The figure is an irregular polygon so there is no formula for calculating the perimeter. However, the figure shows vertical and horizontal symmetry which means sides are marked as having the same lengths as other sides. Add the lengths of all of the sides. 𝑃 = 4 + 2 + 2 + 4 + 2 + 2 = 16 The unit is cm. Answer: 16 cm
21. What is the perimeter of the irregular polygon below?
21 © MathTutorDVD.com
The markings on the figure show that all sides have the same length. The figure has 14 sides, so the perimeter can be calculated using the formula 𝑃 = 14𝑠 where 𝑃 is the perimeter and 𝑠 is the length of each side. Thus, 𝑃 = 14(3) = 42. The unit is cm. Answer: 42 cm
22 © MathTutorDVD.com
