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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms 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: MG2.2, MG2.4, and MG3.2 California Standards

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms Perimeter is the distance around a polygon. To find the perimeter of any polygon, you add the lengths of all its sides. Since opposite sides of a parallelogram are equal in length, you can find a formula for the perimeter of a parallelogram. P = w + l + w + l = w + w + l + l = 2w + 2 l w l

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms Additional Example 1: Finding the Perimeter of Parallelograms A. Find the perimeter of the figure. 5 14 P = 2w + 2 l = 2(5) + 2(14) Perimeter of a parallelogram. = 10 + 28 = 38 units Substitute 5 for w and 14 for l.

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms Additional Example 1: Finding the Perimeter of Parallelograms 20 16 B. Find the perimeter of the figure. P = 2w + 2 l = 2(16) + 2(20) Perimeter of a parallelogram. = 32 + 40 = 72 units Substitute 16 for w and 20 for l.

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms 6 11 Check It Out! Example 1 A. Find the perimeter of the figure. P = 2w + 2 l = 2(6) + 2(11) Perimeter of a parallelogram. = 12 + 22 = 34 units Substitute 6 for w and 11 for l.

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms 13 5 Check It Out! Example 1 B. Find the perimeter of the figure. P = 2w + 2 l = 2(5) + 2(13) Perimeter of a parallelogram. = 10 + 26 = 36 units Substitute 5 for w and 13 for l.

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms The area of a plane figure is the number of unit squares needed to cover the figure. The base of a parallelogram is the length of one side. The height is the perpendicular distance from the base to the opposite side. Height Side Base

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms While perimeter is expressed in linear units, such as inches (in.) or meters (m), area is expressed in square units, such as square feet (ft 2 ). You can cut a parallelogram and shift the cut piece to form a rectangle whose base and height are the same as those of the original parallelogram. The same number of unit squares are needed to cover the two figures. So a parallelogram and a rectangle that have the same base and height have the same area.

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms Since the base and height of a rectangle are the same as its length and width, the formula for the area of a rectangle can also be written as A = lw. Helpful Hint

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms A. (–1, –2), (2, –2), (2, 3), (–1, 3) A = 15 units 2 A = 3 5 A = bh Additional Example 2: Using a Graph to Find Area Graph and find the area of the figure with the given vertices. Area of a rectangle. Substitute 3 for b and 5 for h.

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms The height of a parallelogram is not the length of its slanted side. The height of a figure is always perpendicular to the base. Caution!

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms B. (0, 0), (5, 0), (6, 4), (1, 4) Additional Example 2: Using a Graph to Find Area A = 20 units 2 A = 5 4 A = bh Area of a parallelogram. Substitute 5 for b and 4 for h. Graph and find the area of the figure with the given vertices.

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms Check It Out! Example 2 A. (–3, –2), (1, –2), (1, 3), (–3, 3) A = 20 units 2 A = 4 5 A = bh Area of a rectangle. Substitute 4 for b and 5 for h. x y (–3, –2) (1, –2) (1, 3) (–3, 3) 4 5 Graph and find the area of the figure with the given vertices.

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms B. (–1, –1), (3, –1), (5, 3), (1, 3) Check It Out! Example 2 Graph the figure with the given vertices. Then find the area of the figure. (5, 3) x y (–1, –1) (3, –1) (1, 3) 4 4 A = 16 units 2 A = 4 4 A = bh Area of a parallelogram. Substitute 4 for b and 4 for h.

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms A composite figure is made up of basic geometric shapes such as rectangles, triangles, trapezoids, and circles. To find the area of a composite figure, find the areas of the geometric shapes and then add the areas.

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms Additional Example 3: Finding Area and Perimeter of a Composite Figure Find the perimeter and area of the figure. The length of the side that is not labeled is the same as the sum of the lengths of the sides opposite, 18 units. P = 5 + 6 + 3 + 6 + 3 + 6 + 5 + 18 = 52 units 5 5 3 3 6 66

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms 5 5 3 3 6 Add the areas together. A = 6 5 + 6 2 + 6 5 = 30 + 12 + 30 = 72 units 2 66 Additional Example 3 Continued

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms Check It Out! Example 3 7 4 6 2 6 4 ? 7 2 Find the perimeter of the figure. P = 6 + 2 + 4 + 7 + 6 + 4 + 2 + 2 + 2 + 7 = 42 units The length of the side that is not labeled is 2. 2

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Holt CA Course 1 9-1 Perimeter & Area of Parallelograms 7 4 6 2 6 4 2 7 2 Find the area of the figure. 2 6 2 2 7 2 + 2 4 ++ Add the areas together. = 12 + 14 + 4 + 8 A = 2 6 + 7 2 + 2 2 + 4 2 = 38 units 2 Check It Out! Example 3 Continued 2 2

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