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Published byPhillip Williams Modified over 5 years ago

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Warm Up Graph the line segment for each set of ordered pairs. Then find the length of the line segment. 1. (–7, 0), (0, 0) 2. (0, 3), (0, 6) 3. (–4, –2), (1, –2) 7 units 3 units 5 units

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California Standards 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

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Vocabulary perimeter area base height composite figure

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**Perimeter is the distance around a polygon**

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 + 2l w l

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**A. Find the perimeter of the figure.**

5 14 P = 2w + 2l Perimeter of a parallelogram. = 2(5) + 2(14) Substitute 5 for w and 14 for l. = = 38 units

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**B. Find the perimeter of the figure.**

20 16 P = 2w + 2l Perimeter of a parallelogram. = 2(16) + 2(20) Substitute 16 for w and 20 for l. = = 72 units

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**The area of a plane figure is the number of unit squares needed to cover the figure.(units squared)**

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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**Graph and find the area of the figure with the given vertices.**

Area of a rectangle. A = bh Substitute 3 for b and 5 for h. A = 3 • 5 A = 15 units2

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**The height of a parallelogram is not the length of its slanted side**

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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**Graph and find the area of the figure with the given vertices.**

B. (0, 0), (5, 0), (6, 4), (1, 4) Area of a parallelogram. A = bh Substitute 5 for b and 4 for h. A = 5 • 4 A = 20 units2

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**Graph and find the area of the figure with the given vertices.**

x y (–3, –2) (1, –2) (1, 3) (–3, 3) 4 5 Area of a rectangle. A = bh Substitute 4 for b and 5 for h. A = 4 • 5 A = 20 units2

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**Area of a parallelogram.**

Graph the figure with the given vertices. Then find the area of the figure. B. (–1, –1), (3, –1), (5, 3), (1, 3) (5, 3) x y (–1, –1) (3, –1) (1, 3) 4 Area of a parallelogram. A = bh Substitute 4 for b and 4 for h. A = 4 • 4 A = 16 units2

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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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Find the perimeter. 6 6 3 3 6 5 5 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 = = 52 units

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Find the Area: 6 6 3 3 6 5 5 A = 6 • • • 5 Add the areas together. = = 72 units2

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**The length of the side that is not labeled is 2.**

Find the perimeter. The length of the side that is not labeled is 2. 2 4 6 7 7 2 6 2 P = ? = 42 units 4

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**Find the area. Add the areas together.**

2 4 6 7 Add the areas together. A = 2 • • • • 2 7 2 2 6 = 2 2 = 38 units2 2 6 4 2 4 7 2 2 + + +

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Lesson Quiz: Part I 1. Find the perimeter of the figure. 44 ft 2. Find the area of the figure. 108 ft2

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Lesson Quiz: Part II Graph and find the area of each figure with the given vertices. 3. (–4, 2), (6, 2), (6, –3), (–4, –3) 50 units2

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Lesson Quiz: Part III Graph and find the area of each figure with the given vertices. 4. (4, –2), (–2, –2), (–3, 5), (3, 5) 42 units2

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