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Find the area of trapezoids.

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Trapezoid Base of a trapezoid Height of a trapezoid

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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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b 1 =base 1 b 2 =base 2 h=height What is the area of this triangle? What is the area of this trapezoid?

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COPY THIS! h=height b 2 =base 2 b 1 =base 1 What is the area of this trapezoid?

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PASTE HERE! h=height b 2 =base 2 b 1 =base 1 What is the area of this trapezoid?

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h=height FLIP VERTICALLY! b 2 =base 2 b 1 =base 1 What is the area of this trapezoid?

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h=height FLIP HORIZONTALLY! b 2 =base 2 b 1 =base 1 What is the area of this trapezoid?

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h=height TRANSLATE TO HERE! b 2 =base 2 b 1 =base 1 What is the area of this trapezoid?

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h=height CHECK MEASUREMENTS! b 2 =base 2 b 1 =base 1 What is the area of this trapezoid? b 1 =base 1

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

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h=height b 2 =base 2 b 1 =base 1 Area trapezoid = ½ height(base 1 + base 2)

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h=height b 2 =base 2 b 1 =base 1 Area trapezoid = ½ h(b 1 + b 2 )

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Words: Area = ½(height)(base 1 +base 2 ) Symbols: A = 1/2h(b 1 +b 2 )

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

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Your Turn: ANSWER 63 m 2 Find the area of the trapezoid. ANSWER 182 ft 2 ANSWER 50 cm 2 1. 2. 3.

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

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Your Turn: ANSWER h = 7 ft ANSWER b 1 = 5 cm ANSWER b 2 = 8 in. A gives the area of the trapezoid. Find the missing measure. 1. A = 77 ft 2 2. A = 39 cm 2 3. A = 84 in. 2 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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Pg. 448 – 450: #1 – 15 odd, 19 – 37 odd

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