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Area of Trapezoids

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Goal Find the area of trapezoids.

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Key Vocabulary Trapezoid Base of a trapezoid Height of a trapezoid

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Trapezoid A trapezoid is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base. The nonparallel sides are called legs. Height of the trapezoid is the shortest distance (perpendicular distance) between the bases.

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**What is the area of this trapezoid?**

Area of Trapezoid b1=base 1 h=height What is the area of this triangle? What is the area of this trapezoid? b2=base 2

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**What is the area of this trapezoid?**

Area of Trapezoid b1=base 1 h=height What is the area of this trapezoid? b2=base 2 COPY THIS!

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**What is the area of this trapezoid?**

Area of Trapezoid b1=base 1 h=height What is the area of this trapezoid? b2=base 2 PASTE HERE!

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**What is the area of this trapezoid?**

Area of Trapezoid b1=base 1 h=height What is the area of this trapezoid? b2=base 2 FLIP VERTICALLY!

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**What is the area of this trapezoid?**

Area of Trapezoid b1=base 1 h=height What is the area of this trapezoid? b2=base 2 FLIP HORIZONTALLY!

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**What is the area of this trapezoid?**

Area of Trapezoid b1=base 1 h=height What is the area of this trapezoid? b2=base 2 TRANSLATE TO HERE!

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**What is the area of this trapezoid?**

Area of Trapezoid b1=base 1 h=height What is the area of this trapezoid? b2=base 2 b1=base 1 CHECK MEASUREMENTS!

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**Area of the trapezoid is ½ the area of this parallelogram?**

Area of Trapezoid b1=base 1 Area of the trapezoid is ½ the area of this parallelogram? h=height b2=base 2 b1=base 1

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**Area of Trapezoid b1=base 1 h=height Areatrapezoid =**

½ height(base 1 + base 2) b2=base 2 b1=base 1

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**Areatrapezoid = ½ h(b1 + b2)**

Area of Trapezoid b1=base 1 h=height Areatrapezoid = ½ h(b1 + b2) b2=base 2 b1=base 1

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**Area of Trapezoid Words: Area = ½(height)(base1+base2)**

Symbols: A = 1/2h(b1+b2)

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**Find the area of the trapezoid.**

Example 1 Find the Area of a Trapezoid Find the area of the trapezoid. SOLUTION Formula for the area of a triangle A = h(b1 + b2) 1 2 = 1 2 (5)(6 + 8) Substitute 5 for h, 6 for b1, and 8 for b2. = 1 2 (5)(14) Simplify within parentheses. = 35 Simplify. ANSWER The area of the trapezoid is 35 square inches. 16

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Your Turn: Find the area of the trapezoid. 1. ANSWER 63 m2 2. ANSWER 182 ft2 3. ANSWER 50 cm2

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Example 2 Use the Area of a Trapezoid Find the value of b2 given that the area of the trapezoid is 96 square meters. SOLUTION A = 1 2 h(b1 + b2) Formula for the area of a trapezoid 1 2 (8)(9 + b2) 96 = Substitute 96 for A, 8 for h, and 9 for b1. 192 = 8(9 + b2) Multiply each side by 2. 192 = b2 Use the distributive property. 120 = 8b2 Subtract 72 from each side. 15 = b2 Divide each side by 8. ANSWER The value of b2 is 15 meters. 18

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Your Turn: A gives the area of the trapezoid. Find the missing measure. 1. A = 77 ft2 ANSWER h = 7 ft 2. A = 39 cm2 ANSWER b1 = 5 cm 3. A = 84 in.2 ANSWER b2 = 8 in. A trapezoid has an area of 294 square yards. Its height is 14 yards and the length of one base is 30 yards. Find the length of the other base. 4. ANSWER 12 yards

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Assignment Pg. 448 – 450: #1 – 15 odd, 19 – 37 odd

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Entry Task Find the unknown side length in each right triangle with legs a and b and hypotenuse c. 1. a = 20, b = 21 2. b = 21, c = 35 c = 29 a = 28.

Entry Task Find the unknown side length in each right triangle with legs a and b and hypotenuse c. 1. a = 20, b = 21 2. b = 21, c = 35 c = 29 a = 28.

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