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Comprehensive Guide to Area Calculation and Right Triangle Properties

This chapter explores fundamental concepts in geometry, focusing on the areas of different shapes, including equilateral triangles, squares, regular hexagons, parallelograms, right triangles, rhombuses, and trapezoids. It also covers the Pythagorean Theorem and how to form right triangles using given segment lengths. The chapter emphasizes formulas for calculating areas, circumferences of circles, and relationships among triangle dimensions, facilitating a deep understanding of geometric properties.

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Comprehensive Guide to Area Calculation and Right Triangle Properties

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  1. Chapter 7

  2. SIMPLIFY: 20 12 3

  3. 20 = 4 5 = 2 512312 3 3 3 3 = = 4 3

  4. MULTIPLY:( 2 5 )2

  5. (2 5 )2 = 4 25 = 4 5 = 20 .

  6. COMPLETE:( ___ )2 + ( ___ )2 = ( ___ )2 hyp leg1 leg2

  7. (leg1)2 + (leg2)2 = (hyp)2 • Pythagorean Theorem

  8. Complete to form RIGHT triangles: 3, 4, ____ 5, 12, ____ 6, 8, ____ 8, 15, ____

  9. 3, 4, 5 5, 12, 13 6, 8, 10 8, 15, 17

  10. Given segment lengths a, b, c longest Right c2 a2 + b2 Obtuse c2 a2 + b2 Acute c2 a2 + b2

  11. Right c2= a2 + b2 Obtuse c2> a2 + b2 Acute c2< a2 + b2

  12. COMPLETE: • L = ____ • H = ____ 45 45

  13. L = LH =L 2

  14. SOLVE: 45 • x = _____ • y = _____ y 8 45 x

  15. x = 8y = 8 2

  16. COMPLETE: • LL = _____ • H = _____ 60 Ls 30

  17. LL = Ls 3H = 2 Ls

  18. SOLVE: y x = _____ y = _____ 60 4 30 x

  19. x = 4 3y = 8

  20. AREA OF EQUILATERAL TRIANGLES: A = ½ ( ____ )( ____ ) A = ½ ( ____)( ____ ) A = ( ____ )2 ( ____ )

  21. A = ½ bh A = ½ ap A = s2 4

  22. Find the area: 6 (Equilateral Triangle)

  23. 18 6 3 30 9 A = s2 4 A = (18)2 4 A = 81 A = ½ bh A = ½ (18)(9 ) A = 81 A = ½ ap A = ½ (3 )(54) A = 81

  24. AREA OF SQUARES: • A = ( ____ )2 • A = ½ ( ____ )( ____ ) • A = ½ ( ____ )( ____ )

  25. A = s2 A = ½ ap A = ½ d1d2 a side (s)

  26. Find the area: 10 (Square)

  27. 20 10 10 45 10 A = s2 A = 202 A = 400 A = ½ ap A = ½ (10)(80) A = 400 A = ½ d1d2 A = ½ (20 )(20 ) A = 400

  28. AREA OF REGULAR HEXAGONS:A = ½ ( ____ )( ____ )

  29. A = ½ ap 120 a 60

  30. Find the area: 8 (Regular Hexagon)

  31. 8 4 3 60 4 4 A = ½ ap A = ½ (4 3)(48) A = 96 3

  32. AREA OF PARALLELOGRAMS: • A = ( ____ )( ____ )

  33. A = bh Height (h) Base (b)

  34. AREA OF ANY TRIANGLE:A = ½ ( ____ )( ____ )

  35. A = ½bh height (h) base (b)

  36. Find the height: 6 6 4

  37. 6 6 h 2 2 4 h2 +22 =62h2 = 32h = 32 = 4 2

  38. AREA OF RIGHT TRIANGLES:A = ½ ( ____ )( ____ )

  39. A = ½ (l1)(l2) leg (l1) leg (l2)

  40. AREA OF RHOMBUSES: • A = ½ ( ____ ) ( ____ )

  41. A = ½ (d1)(d2)

  42. AREA OF TRAPEZOIDS: A = ½ ( ____ ) ( ____ + ____ )

  43. A = ½(h)(b1+ b2) base (b1) height (h) base(b2)

  44. FOR CIRCLES: Circumference = ( __ )( __ )( __ )

  45. C = 2rπ

  46. What fraction of the circumference is arc AB? r B 120o A

  47. 120= 1 360 3

  48. AREA OF CIRCLES: A = ( ____ )( ____ )2

  49. A = πr2

  50. What fraction of the circle is shaded? 450 r

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