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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids MG2.1 Use formulas routinely for finding the perimeter and area of basic two- dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Also covered: MG3.2 California Standards

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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids Additional Example 1: Using Perimeter 71 = 55 + d d = 16 in. P = 22 + 15 + 18 + d 16 = d Substitute 71 for P. Find the missing measurement when the perimeter is 71 in. 18 in. 22 in. 15 in. Subtract 55 from both sides. 55 d

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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids Check It Out! Example 1 58 = 49 + d d = 9 in. P = 28 + 7 + 14 + d 9 = d Substitute 58 for P. Find the missing measurement when the perimeter is 58 in. 14 in. 28 in. 7 in. Subtract 49 from both sides. 49 d

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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids Additional Example 2: Multi-Step Application Step 1: Find the length of the third side. Substitute 12 for a and 20 for c. 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? b = 16 a 2 + b 2 = c 2 12 2 + b 2 = 20 2 144 + b 2 = 400 b 2 = 256 Use the Pythagorean Theorem. √256 = 16.

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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids Additional Example 3 Continued Step 2: Find the perimeter of the yard. Add all sides. P = a + b + c = 12 + 20 + 16 = 48 The border will be 48 feet long.

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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids Check It Out! Example 2 Step 1: Find the length of the third side. Substitute 38 for a and 32 for b. A gardener wants to plant a border of flowers around the building that is in the shape of a right triangle. He knows that the length of the shortest sides of the building are 38 feet and 32 feet. How long will the border be? c ≈ 49.68 a 2 + b 2 = c 2 38 2 + 32 2 = c 2 1444 + 1024 = c 2 2468 = c 2 Use the Pythagorean Theorem. √2468 49.68.

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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids Check It Out! Example 2 Continued Step 2: Find the perimeter of the yard. Add all sides. P = a + b + c 38 + 32 + 49.68 119.68 The border will be about 119.68 feet long.

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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids A triangle or trapezoid can be thought of as half of a parallelogram. Therefore, the formulas for the area of a triangle or trapezoid have as a factor. 1212

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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids

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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids A. (–2, 2), (4, 2), (0, 5) x y 6 3 = 9 units 2 A = bh 1212 Additional Example 3: Finding the 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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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids B. (–1, 1), (4, 1), (4, 4), (0, 4) = 13.5 units 2 A = h(b 1 + b 2 ) 1212 = 3(5 + 4) 1212 Area of a trapezoid Substitute for h, b 1, and b 2. (–1, 1) (0, 4) (4, 4) x y (4, 1) Graph and find the area of the figure with the given vertices. Additional Example 3: Finding the Area of Triangles and Trapezoids 5 3 4

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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids A. (–1, –2), (5, –2), (5, 2), (–1, 6) Check It Out! Example 3 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

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Holt CA Course 1 9-2 Perimeter and Area of Triangles and Trapezoids B. (–1, 1), (5, 1), (1, 5) x y 6 4 = 12 units 2 A = bh 1212 Check It Out! Example 3 Graph and find the area of the figure with the given vertices. (5, 1) (1, 5) (–1, 1) = 6 4 1212 Area of a triangle Substitute for b and h.

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