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Area of Trapezoids

Area of Trapezoids. Goal. Find the area of trapezoids. Key Vocabulary. Trapezoid Base of a trapezoid Height of a trapezoid. Trapezoid. A trapezoid is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base .

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Area of Trapezoids

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  1. Area of Trapezoids

  2. Goal • Find the area of trapezoids.

  3. Key Vocabulary • Trapezoid • Base of a trapezoid • Height of a trapezoid

  4. Trapezoid • A trapezoidis 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.

  5. 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

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

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

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

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

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

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

  12. 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

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

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

  15. Area of Trapezoid • Words: Area = ½(height)(base1+base2) • Symbols: A = 1/2h(b1+b2)

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

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

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

  19. Your Turn: Agives the area of the trapezoid. Find the missing measure. 1. A = 77 ft2 2. A = 39 cm2 b2 = 8 in. b1 = 5 cm h = 7 ft 12 yards ANSWER ANSWER ANSWER ANSWER 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.

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

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