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The Area of a Trapezoid Lesson 11.3

b 2. h. b 1. The Area of a Trapezoid Lesson 11.3. Theorem 102: The area of a trapezoid equals one-half the product of the height and the sum of the bases. A trap = h(b 1 + b 2 ). Where b 1 is the length of one base, b 2 is the length of the other base, and h is the height.

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The Area of a Trapezoid Lesson 11.3

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  1. b2 h b1 The Area of a TrapezoidLesson 11.3

  2. Theorem 102: The area of a trapezoid equals one-half the product of the height and the sum of the bases. Atrap = h(b1 + b2) Where b1is the length of one base, b2is the length of the other base, and h is the height.

  3. Prove that the area of a trapezoid is ½ h(b1 + b2) by the following method: Group A Group B Draw altitudes and use the rectangle and triangles formed. • Draw a diagonal and use the two triangles formed.

  4. Median of a Trapezoid The line segment joining the midpoints of the non-parallel sides of a trapezoid is called the median of the trapezoid. C L Y X Z E U

  5. Theorem 103: The measure of the median of a trapezoid equals the average of the measures of the bases. M = (b1 + b2) Where b1 is the length of one base and b2 is the length of the other base.

  6. Theorem 104: The area of a trapezoid is the product of the median and the height. Atrap = Mh Where M is the length of the median and h is the height.

  7. Find the area. x > 60˚ • Find h. • h = 3√3 • Find x. • 3 • Find b1. • 3 + 3 + 7 = 13 h 6in. > 7in. A = ½ h(b1 + b2) A = ½ (3√3)(13 + 7) A =30√3 in2

  8. Find the median & area of the trapezoid. 6 M Median = ½(b1 + b2) M = ½(14 + 6) M = 10 12 14 A = Mh A = 10(12) A = 120

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