Chapter 9 — Answers

Selected answers for Chapter 9: Area, transcribed from the book’s appendix. They are meant for checking your work, not for copying — the book prints answers to selected exercises only.

Back to Chapter 9 · Teacher’s answers: Chapter 9 · Complete key: Answers to Exercises PDF · Printed answers: appendices PDF

Lesson 1 (pages 340–342)

3. Its area is equal to the sum of the areas of its nonoverlapping parts.

7. True, because △ADC ≅ △ABC.

9. True, because $a_{\triangle ADC}-a_{\triangle1}-a_{\triangle2}=a_{\triangle ABC}-a_{\triangle4}-a_{\triangle3}$.

14. $2x$ square units.

16. $(x+y)$ square units.

20. They are both concave octagons.

23. $3a+6b$.

26. They are congruent (SSS)

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and therefore equal in area.

30. No.

31. Yes. Each one contains two of the four triangles, all of whose areas are equal.

35. $\dfrac{1}{6}$ square unit.

37. 2 square units.

42. It is equilateral and equiangular.

43. BFED contains four of the congruent triangles, and ABCD contains two of them.

44. 4 square units.

49. They are both equal to AB.

50. Because DF = DC + CF = CF + FE = CE.

Lesson 2 (pages 345–349)

1. 20 ft.

4. 3,600 in².

8. Four.

11. $a(b+c)$.

12. $ab$ and $ac$.

14. $(a+b)^2$.

19. Two congruent triangles.

22. $\sqrt{26}$.

25. No.

28. 2,592 nails.

30. 66 ft.

34. 6,400 square chains.

37. 84 cm².

38. 17.5%.

40. 21.6 ft long.

43. The total surface area of the walls.

47. 1,728 in².

48. 189 in².

Lesson 3 (pages 353–357)

1. 6 square units.

5. $\dfrac{1}{4}c^2$.

6. The area of a right triangle is half the product of its legs.

7. The area of a polygonal region is equal to the sum of the areas of its nonoverlapping parts (the Area Postulate).

9. Substitution.

15. They seem to be equal.

17. △ABC, 40 units; △DEF, 80 units.

21. They seem to stay the same.

27. $\alpha_{ABCD}\approx99.87$ square chains.

29. The area of a triangle is half the product of any base and corresponding altitude.

31. Substitution.

33. Division.

35. 84 square units.

36. 11.2 units.

41. In a plane, two points each equidistant from the endpoints of a line segment determine the perpendicular bisector of the line segment.

42. Betweenness of Points Theorem.

48. $\alpha_{\triangle AMB}=\alpha_{\triangle AMD}=20.25$ in²; $\alpha_{\triangle BMX}=\alpha_{\triangle DMY}=6.75$ in²; $\alpha_{\triangle CMX}=\alpha_{\triangle CMY}=13.5$ in².

52. About 1,200 shingles.

Lesson 4 (pages 360–364)

1. That they are equal.

2. 2,800 ft².

6. Area = $\dfrac{1}{4}(s+s)(s+s)=\dfrac{1}{4}(2s)(2s)=s^2$.

8. 260 square units.

14. 1,369 square units.

17. A parallelogram. (Two of its opposite sides are both parallel and equal.)

18. 1 unit. $A=bh=(1)(1)=1$.

23. 30,794 ft².

26. 4.5 ft².

28. 8.25 ft².

32. 675 m².

35. 3,696 m².

41. Its area is $(a+b)h$.

43. In a plane, two lines perpendicular to a third line are parallel.

46. 165 square units.

50. △EBH, FHCG (and FHCD).

Lesson 5 (pages 367–370)

2. 2, 2, and 4 units.

4. The Ruler Postulate.

5. The Protractor Postulate.

8. The square of the hypotenuse of a right triangle is equal to the sum of the squares of its legs.

9. Substitution.

12. Substitution.

15. 12.

16. 1,225.

18. 37.

26. No. $256+225=481\neq484$.

33. 6 units.

35. 25 units.

37. $2ab$.

38. $(b-a)^2$.

43. The acute angles of a right triangle are complementary (so the sum of these angles is 90°).

45. A trapezoid.

49. It appears to bisect ABDE (that is, divide it into two congruent parts having equal areas).

Review (pages 371–375)

1. 125 m².

3. 525.

4. Camp A, 68 paces; camp B, 64 paces; camp C, 60 paces.

8. 16 units.

12. The area of a polygonal region is equal to the sum of the areas of its nonoverlapping parts.

14. ∠DEY.

16. AAS.

18. Corresponding parts of congruent triangles are equal.

20. Triangles with equal bases and equal altitudes have equal areas.

23. 11.

27. $4a$.

29. $4a+4b$.

30. $a(a+2b)$ or $a^2+2ab$.

34. 216 ft².

38. 332.5 ft².

40. It would be four times as great.

44. $\alpha_{\triangle AEF}=2x$ (because AF = 2AC and BH = EG).

46. $4x^2-xy$.

47. $4x-y$.

51. It would be rectangular.

Algebra Review (page 376)

1. 500.

2. $\dfrac{1}{5}$ or 0.2.

3. 2.5.

4. ±10.

5. −3.

6. 42.

7. 15.

8. 20.

9. 41.

10. 3.5.

11. 0.

12. 8.

13. 5.

14. 5.

15. −36.

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