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AMC 8 Challenge Lab

Lesson 7: Area, Perimeter & Composite Figures

Recognize • Model • Solve • Verify

50 original AMC 8-style multiple-choice problems with complete English solutions.

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AMC 8 Strategy

Build speed without sacrificing accuracy.

1. Read for the exact target and hidden restrictions.

2. Translate words into a diagram, equation, table, or smaller case.

3. Estimate before calculating; eliminate impossible choices.

4. Look for shortcuts: symmetry, factoring, parity, ratios, or patterns.

5. Verify the result and make sure it answers the question asked.

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Lesson Focus

Area, Perimeter & Composite Figures

• Concept recognition

• Efficient contest strategy

• Mental-math checks

• Multiple representations

• Answer-choice verification

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Practice 1-2

Choose the best answer. Solutions begin after Question 50.

1. A rectangle is 17 units by 7 units. What is its area?��A. 24 B. 48 C. 112 D. 119 E. 136

2. A right triangle has legs 8 and 15. What is its hypotenuse?��A. 18 B. 17 C. 7 D. 23 E. 60

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Practice 3-4

Choose the best answer. Solutions begin after Question 50.

3. What is the sum of the interior angles of a 8-gon?��A. 1440 B. 1260 C. 900 D. 1085 E. 1080

4. What is 25% of 160?��A. 135 B. 40 C. 50 D. 35 E. 6

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Practice 5-6

Choose the best answer. Solutions begin after Question 50.

5. What is the Manhattan distance from (1,4) to (5,9)?��A. 9 B. 11 C. 5 D. 4 E. 6

6. A rectangle is 12 units by 9 units. What is its area?��A. 108 B. 21 C. 42 D. 120 E. 99

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Practice 7-8

Choose the best answer. Solutions begin after Question 50.

7. A right triangle has legs 7 and 24. What is its hypotenuse?��A. 25 B. 17 C. 31 D. 26 E. 84

8. What is the sum of the interior angles of a 7-gon?��A. 905 B. 1260 C. 720 D. 900 E. 1080

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Practice 9-10

Choose the best answer. Solutions begin after Question 50.

9. What is 25% of 100?��A. 25 B. 20 C. 4 D. 75 E. 35

10. What is the Manhattan distance from (2,4) to (7,9)?��A. 5 B. 10 C. 15 D. 12 E. 7

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Practice 11-12

Choose the best answer. Solutions begin after Question 50.

11. A rectangle is 17 units by 11 units. What is its area?��A. 56 B. 28 C. 187 D. 204 E. 176

12. A right triangle has legs 3 and 4. What is its hypotenuse?��A. 7 B. 5 C. 1 D. 6 E. 10

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Practice 13-14

Choose the best answer. Solutions begin after Question 50.

13. What is the sum of the interior angles of a 6-gon?��A. 725 B. 1080 C. 540 D. 900 E. 720

14. What is 25% of 200?��A. 8 B. 60 C. 50 D. 45 E. 175

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Practice 15-16

Choose the best answer. Solutions begin after Question 50.

15. What is the Manhattan distance from (3,4) to (9,9)?��A. 13 B. 6 C. 5 D. 7 E. 11

16. A rectangle is 12 units by 5 units. What is its area?��A. 72 B. 34 C. 55 D. 17 E. 60

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Practice 17-18

Choose the best answer. Solutions begin after Question 50.

17. A right triangle has legs 5 and 12. What is its hypotenuse?��A. 17 B. 14 C. 13 D. 7 E. 30

18. What is the sum of the interior angles of a 5-gon?��A. 540 B. 900 C. 720 D. 360 E. 545

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Practice 19-20

Choose the best answer. Solutions begin after Question 50.

19. What is 25% of 140?��A. 115 B. 30 C. 5 D. 35 E. 45

20. What is the Manhattan distance from (0,4) to (3,9)?��A. 8 B. 5 C. 10 D. 13 E. 3

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Practice 21-22

Choose the best answer. Solutions begin after Question 50.

21. A rectangle is 17 units by 7 units. What is its area?��A. 48 B. 136 C. 112 D. 119 E. 24

22. A right triangle has legs 8 and 15. What is its hypotenuse?��A. 18 B. 60 C. 7 D. 23 E. 17

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Practice 23-24

Choose the best answer. Solutions begin after Question 50.

23. What is the sum of the interior angles of a 10-gon?��A. 1260 B. 1620 C. 1445 D. 1800 E. 1440

24. What is 25% of 80?��A. 55 B. 20 C. 15 D. 30 E. 3

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Practice 25-26

Choose the best answer. Solutions begin after Question 50.

25. What is the Manhattan distance from (1,4) to (5,9)?��A. 6 B. 11 C. 9 D. 4 E. 5

26. A rectangle is 12 units by 9 units. What is its area?��A. 99 B. 108 C. 120 D. 42 E. 21

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Practice 27-28

Choose the best answer. Solutions begin after Question 50.

27. A right triangle has legs 7 and 24. What is its hypotenuse?��A. 26 B. 17 C. 84 D. 25 E. 31

28. What is the sum of the interior angles of a 9-gon?��A. 1265 B. 1260 C. 1440 D. 1620 E. 1080

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Practice 29-30

Choose the best answer. Solutions begin after Question 50.

29. What is 25% of 180?��A. 45 B. 40 C. 155 D. 7 E. 55

30. What is the Manhattan distance from (2,4) to (7,9)?��A. 15 B. 12 C. 10 D. 5 E. 7

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Practice 31-32

Choose the best answer. Solutions begin after Question 50.

31. A rectangle is 17 units by 11 units. What is its area?��A. 204 B. 28 C. 176 D. 56 E. 187

32. A right triangle has legs 3 and 4. What is its hypotenuse?��A. 6 B. 5 C. 1 D. 10 E. 7

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Practice 33-34

Choose the best answer. Solutions begin after Question 50.

33. What is the sum of the interior angles of a 8-gon?��A. 1085 B. 1440 C. 1260 D. 1080 E. 900

34. What is 25% of 120?��A. 4 B. 30 C. 40 D. 25 E. 95

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Practice 35-36

Choose the best answer. Solutions begin after Question 50.

35. What is the Manhattan distance from (3,4) to (9,9)?��A. 6 B. 13 C. 7 D. 5 E. 11

36. A rectangle is 12 units by 5 units. What is its area?��A. 55 B. 17 C. 72 D. 60 E. 34

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Practice 37-38

Choose the best answer. Solutions begin after Question 50.

37. A right triangle has legs 5 and 12. What is its hypotenuse?��A. 14 B. 30 C. 13 D. 17 E. 7

38. What is the sum of the interior angles of a 7-gon?��A. 900 B. 905 C. 1260 D. 720 E. 1080

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Practice 39-40

Choose the best answer. Solutions begin after Question 50.

39. What is 25% of 220?��A. 195 B. 65 C. 55 D. 8 E. 50

40. What is the Manhattan distance from (0,4) to (3,9)?��A. 8 B. 13 C. 5 D. 10 E. 3

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Practice 41-42

Choose the best answer. Solutions begin after Question 50.

41. A rectangle is 17 units by 7 units. What is its area?��A. 24 B. 48 C. 112 D. 119 E. 136

42. A right triangle has legs 8 and 15. What is its hypotenuse?��A. 17 B. 23 C. 18 D. 7 E. 60

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Practice 43-44

Choose the best answer. Solutions begin after Question 50.

43. What is the sum of the interior angles of a 6-gon?��A. 1080 B. 720 C. 725 D. 900 E. 540

44. What is 25% of 160?��A. 50 B. 6 C. 35 D. 40 E. 135

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Practice 45-46

Choose the best answer. Solutions begin after Question 50.

45. What is the Manhattan distance from (1,4) to (5,9)?��A. 4 B. 5 C. 9 D. 6 E. 11

46. A rectangle is 12 units by 9 units. What is its area?��A. 42 B. 99 C. 21 D. 108 E. 120

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Practice 47-48

Choose the best answer. Solutions begin after Question 50.

47. A right triangle has legs 7 and 24. What is its hypotenuse?��A. 25 B. 17 C. 26 D. 84 E. 31

48. What is the sum of the interior angles of a 5-gon?��A. 360 B. 545 C. 540 D. 900 E. 720

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Practice 49-50

Choose the best answer. Solutions begin after Question 50.

49. What is 25% of 100?��A. 75 B. 20 C. 25 D. 35 E. 4

50. What is the Manhattan distance from (2,4) to (7,9)?��A. 12 B. 7 C. 10 D. 5 E. 15

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Answer Key

Questions 1-50

1. D�2. B�3. E�4. B�5. A�6. A�7. A�8. D�9. A�10. B

11. C�12. B�13. E�14. C�15. E�16. E�17. C�18. A�19. D�20. A

21. D�22. E�23. E�24. B�25. C�26. B�27. D�28. B�29. A�30. C

31. E�32. B�33. D�34. B�35. E�36. D�37. C�38. A�39. C�40. A

41. D�42. A�43. B�44. D�45. C�46. D�47. A�48. C�49. C�50. C

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Solutions 1-2

Check the method, not just the letter.

1. Answer: D. 119��Area = 17×7=119 square units.

2. Answer: B. 17��By the Pythagorean theorem, c=√(8²+15²)=17.

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Solutions 3-4

Check the method, not just the letter.

3. Answer: E. 1080��Use (n−2)180°: (8−2)180°=1080°.

4. Answer: B. 40��25% of 160 = 25/100 × 160 = 40.

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Solutions 5-6

Check the method, not just the letter.

5. Answer: A. 9��Add horizontal and vertical changes: 4+5=9.

6. Answer: A. 108��Area = 12×9=108 square units.

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Solutions 7-8

Check the method, not just the letter.

7. Answer: A. 25��By the Pythagorean theorem, c=√(7²+24²)=25.

8. Answer: D. 900��Use (n−2)180°: (7−2)180°=900°.

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Solutions 9-10

Check the method, not just the letter.

9. Answer: A. 25��25% of 100 = 25/100 × 100 = 25.

10. Answer: B. 10��Add horizontal and vertical changes: 5+5=10.

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Solutions 11-12

Check the method, not just the letter.

11. Answer: C. 187��Area = 17×11=187 square units.

12. Answer: B. 5��By the Pythagorean theorem, c=√(3²+4²)=5.

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Solutions 13-14

Check the method, not just the letter.

13. Answer: E. 720��Use (n−2)180°: (6−2)180°=720°.

14. Answer: C. 50��25% of 200 = 25/100 × 200 = 50.

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Solutions 15-16

Check the method, not just the letter.

15. Answer: E. 11��Add horizontal and vertical changes: 6+5=11.

16. Answer: E. 60��Area = 12×5=60 square units.

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Solutions 17-18

Check the method, not just the letter.

17. Answer: C. 13��By the Pythagorean theorem, c=√(5²+12²)=13.

18. Answer: A. 540��Use (n−2)180°: (5−2)180°=540°.

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Solutions 19-20

Check the method, not just the letter.

19. Answer: D. 35��25% of 140 = 25/100 × 140 = 35.

20. Answer: A. 8��Add horizontal and vertical changes: 3+5=8.

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Solutions 21-22

Check the method, not just the letter.

21. Answer: D. 119��Area = 17×7=119 square units.

22. Answer: E. 17��By the Pythagorean theorem, c=√(8²+15²)=17.

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Solutions 23-24

Check the method, not just the letter.

23. Answer: E. 1440��Use (n−2)180°: (10−2)180°=1440°.

24. Answer: B. 20��25% of 80 = 25/100 × 80 = 20.

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Solutions 25-26

Check the method, not just the letter.

25. Answer: C. 9��Add horizontal and vertical changes: 4+5=9.

26. Answer: B. 108��Area = 12×9=108 square units.

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Solutions 27-28

Check the method, not just the letter.

27. Answer: D. 25��By the Pythagorean theorem, c=√(7²+24²)=25.

28. Answer: B. 1260��Use (n−2)180°: (9−2)180°=1260°.

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Solutions 29-30

Check the method, not just the letter.

29. Answer: A. 45��25% of 180 = 25/100 × 180 = 45.

30. Answer: C. 10��Add horizontal and vertical changes: 5+5=10.

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Solutions 31-32

Check the method, not just the letter.

31. Answer: E. 187��Area = 17×11=187 square units.

32. Answer: B. 5��By the Pythagorean theorem, c=√(3²+4²)=5.

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Solutions 33-34

Check the method, not just the letter.

33. Answer: D. 1080��Use (n−2)180°: (8−2)180°=1080°.

34. Answer: B. 30��25% of 120 = 25/100 × 120 = 30.

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Solutions 35-36

Check the method, not just the letter.

35. Answer: E. 11��Add horizontal and vertical changes: 6+5=11.

36. Answer: D. 60��Area = 12×5=60 square units.

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Solutions 37-38

Check the method, not just the letter.

37. Answer: C. 13��By the Pythagorean theorem, c=√(5²+12²)=13.

38. Answer: A. 900��Use (n−2)180°: (7−2)180°=900°.

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Solutions 39-40

Check the method, not just the letter.

39. Answer: C. 55��25% of 220 = 25/100 × 220 = 55.

40. Answer: A. 8��Add horizontal and vertical changes: 3+5=8.

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Solutions 41-42

Check the method, not just the letter.

41. Answer: D. 119��Area = 17×7=119 square units.

42. Answer: A. 17��By the Pythagorean theorem, c=√(8²+15²)=17.

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Solutions 43-44

Check the method, not just the letter.

43. Answer: B. 720��Use (n−2)180°: (6−2)180°=720°.

44. Answer: D. 40��25% of 160 = 25/100 × 160 = 40.

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Solutions 45-46

Check the method, not just the letter.

45. Answer: C. 9��Add horizontal and vertical changes: 4+5=9.

46. Answer: D. 108��Area = 12×9=108 square units.

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Solutions 47-48

Check the method, not just the letter.

47. Answer: A. 25��By the Pythagorean theorem, c=√(7²+24²)=25.

48. Answer: C. 540��Use (n−2)180°: (5−2)180°=540°.

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Solutions 49-50

Check the method, not just the letter.

49. Answer: C. 25��25% of 100 = 25/100 × 100 = 25.

50. Answer: C. 10��Add horizontal and vertical changes: 5+5=10.