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1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. Find the area of a parallelogram with height 9 in. and base length 15 in. 2. Find the area of a rectangle with side lengths 24 in. and 32 in. 64 ft 768 in 2 135 in 2 Warm Up

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Pre-Algebra 6.2 Perimeter and Area of Triangles and Trapezoids

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Learn to find the area of triangles and trapezoids.

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The figures show a fractal called the Koch snowflake. It is constructed by first drawing an equilateral triangle. Then triangles with sides one- third the length of the original sides are added to the middle of each side. The second step is then repeated over and over again.

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The area and perimeter of each figure is larger than that of the one before it. However, the area of any figure is never greater than the area of the box, while the perimeters increase without bound. To find the area and perimeter of each figure, you must be able to find the area of a triangle.

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A. 4 10 = 21 units B. = 42 units 7 17 8 11 6 P = 4 + 7 + 10 Add all sides. P = 8 + 11 + 6 + 17 Add all sides. Find the perimeter of each figure. Example: Finding the Perimeter of Triangles and Trapezoids

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A. 6 11 P = 9 + 6 + 11 Add all sides. 9 = 26 units B. 22 5 P = 6 + 22 + 5 + 16 = 49 units Add all sides. 16 6 Find the perimeter of each figure. Try This

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A triangle or trapezoid can be thought of as half of a parallelogram.

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Triangle: The area A of a triangle is one-half the base length b times the height h. AREA OF A TRIANGLE WordsNumbersFormula A = (8)(4) = 16 units 2 1212

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AREA OF A TRAPEZOID WordsNumbersFormula Trapezoid: The area of a trapezoid is one-half the height h times the sum of the base lengths b 1 and b 2. A = (2)(3 + 7) = 10 units 2 1212 A = (h)(b 1 + b 2 ) 1212

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A. (–2, 2), (4, 2), (0, 5) x y 6 3 = 9 units 2 A = bh 1212 Graph and find the area of the figure with the given vertices. (4, 2) (0, 5) (–2, 2) = 6 3 1212 Area of a triangle Substitute for b and h. Example: Finding the Area of Triangles and Trapezoids

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B. (–1, 2), (5, –2), (5, 2), (–1, 6) Graph and find the area of the figure with the given vertices. = 36 units 2 A = h(b 1 + b 2 ) 1212 = 6(8 + 4) 1212 Area of a trapezoid Substitute for h, b 1, and b 2. (–1, –2) (–1, 6) (5, 2) x y (5, –2) 48 6 Example: Finding the Area of Triangles and Trapezoids

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A. (–1, 1), (1, 7), (7, 1) Graph and find the area of the figure with the given vertices. x y 8 (1, 7) (–1, 1) (7, 1) = 24 units 2 A = bh 1212 = 8 6 1212 Area of a triangle Substitute for b and h. 6 Try This

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B. (–2, –1), (0, 5), (3, 5), (5, –1) (–2, –1) (0, 5) (3, 5) x y (5, –1) 3 7 6 Graph and find the area of the figure with the given vertices. = 30 units 2 A = h(b 1 + b 2 ) 1212 = 6(7 + 3) 1212 Area of a trapezoid Substitute for h, b 1, and b 2. Try This

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Use the figure to find the following measurements. 1. The perimeter of the triangle 2. The perimeter of the trapezoid 3. The perimeter of the combined figure 4. The area of the triangle 5. The area of the trapezoid 36 cm 44 cm 54 cm 2 64 cm 104 cm 2 Lesson Quiz

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