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Section 1-7 Perimeter, Area, Circumference SPI 21B: solve equations to find length, width, perimeter and area SPI 32L: determine the area of indicated regions involving figures SPI 41A: determine the perimeter & area of 3 or 4 sided plane figures Objectives: find perimeter and area of rectangles and squares find circumference and area of circles Perimeter: the sum of the lengths of the sides of a polygon fence around a garden Circumference: the distance around the outside of a circle Area: number of units (squared) enclosed by the perimeter or circumference

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Some Common Formulas Square Perimeter: P = 4s Area: A = s 2 Rectangle Perimeter: P = 2b + 2h Area: A = bh b = base h = height s = side Circle d = diameter r = radius Circumference: C = d or C = 2 r Area: A = r 2

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Real-World Connection Fencing. Your pool is depicted in the diagram below. You want to build a fence around the deck. How much fencing will you need? Width of pool and deck: 15 + 3 + 3 = 21 feet Length of pool and deck: 20 + 3 + 3 = 26 feet Solve: P = 2w + 2L Formula = 2(21) + 2(26) Substitute = 94 Simplify You will need 94 feet of fencing.

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Real-World and Finding Circumference Biology. In the Pacific Northwest, a red fox has a circular home range with a radius of about 718 meters. What is the area of the home range of a red fox? A = r 2 Formula A = (718) 2 Substitute = 1,619,566 Simplify

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Finding Perimeter in the Coordinate Plane Find the perimeter of ∆ ABC. Find the length of each side. Side AB. |5 – (-1)| = 6 Side BC. |6- (-2)| = 8 Side AC. AB + BC + AC = 6 + 8 + 10 = 24. The perimeter is 24 units.

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Finding Area of a Rectangle You are designing a banner for a music festival. The banner will be 4 ft wide by 7 feet high. How much material will you need? Area of Rectangle = bh Convert yards to feet: 7 yards = 21 feet Substitute values into formula A = 4(21) = 84 You will need 84 square feet (ft 2 ) of material.

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Finding Area of Irregular Figures Find the area of the figure. Separate the figure into rectangles. Use Area of a Rectangle Formula A 1 = 6 ∙ 2 = 12 A 2 = 4 ∙ 2 = 8 A 3 = 2 ∙ 2 = 4 Total Area = 12 + 8 + 4 = 24 cm 2

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