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Warm Up Course 3 8-2 Perimeter and Area of Triangles and Trapezoids A rectangle has sides lengths of 12 ft and 20 ft. 2. Find the area. 1. Find the perimeter. 64 ft 240 ft 2

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Problem of the Day The area of a rhombus with two 60° angles is 24 in 2. An equilateral triangle is drawn so that one side is a side of the rhombus. What is the area of the triangle? (Hint: You don't have to use a formula.) 60° 12 in 2 Course 3 8-2 Perimeter and Area of Triangles and Trapezoids

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Learn to find the perimeter and area of triangles and trapezoids. Perimeter and Area of Triangles and Trapezoids Course 3 8-2 Perimeter and Area of Triangles and Trapezoids TB P. 394-398

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Additional Example 1: Finding the Perimeter of Triangles and Trapezoids 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. Course 3 8-2 Perimeter and Area of Triangles and Trapezoids Find the perimeter of each figure.

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Additional Example 2: Finding a Missing Measurement 71 = 55 + d d = 16 in. P = 22 + 15 + 18 + d 16 = d Substitute 71 for P. Course 3 8-2 Perimeter and Area of Triangles and Trapezoids Find the missing measurement for the trapezoid with perimeter 71 in. 18 in. 22 in. 15 in. Subtract 55 from both sides. 55 = 55 d

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Additional Example 3: Multi-Step Application Find the length of the third side of the triangle using the Pythagorean Theorem. Substitute 12 for a and 20 for c. Course 3 8-2 Perimeter and Area of Triangles and Trapezoids A homeowner wants to plant a border of shrubs around her yard that is in the shape of a right triangle. She knows that the length of the shortest side of the yard is 12 feet and the length of the longest side is 20 feet. How long will the border be? √256 = 16. b = 16 a 2 + b 2 = c 2 12 2 + b 2 = 20 2 144 + b 2 = 400 b 2 = 256

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Additional Example 3 Continued Find the perimeter of the yard. Add all sides. Course 3 8-2 Perimeter and Area of Triangles and Trapezoids P = a + b + c = 12 + 20 + 16 = 48 The border will be 48 feet long.

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A triangle or trapezoid can be thought of as half of a parallelogram. Course 3 8-2 Perimeter and Area of Triangles and Trapezoids

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Triangle: The area A of a triangle is one-half the base length b times the height h. Course 3 8-2 Perimeter and Area of Triangles and Trapezoids AREA OF A TRIANGLE WordsNumbersFormula A = (8)(4) = 16 units 2 1212

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Course 3 8-2 Perimeter and Area of Triangles and Trapezoids 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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(–2, 2), (4, 2), (0, 5) x y 6 3 = 9 units 2 A = bh 1212 Additional Example 4: Finding the Area of Triangles and Trapezoids Course 3 8-2 Perimeter and Area of Triangles and Trapezoids 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.

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Lesson Quiz 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 Course 3 8-2 Perimeter and Area of Triangles and Trapezoids

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