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Geometry: Perimeter and Area Melissa Kramer Laingsburg High School Laingsburg, Michigan A polygon is a closed plane figure formed by three or more segments Each segment intersects exactly two others at their endpoints. Names of Polygons # of Sides Name 3 Triangle 4 Quadrilateral 5 6 7 Heptagon 8 9 10 Nonagon Names of Polygons # of Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 7 Heptagon 8 9 10 Nonagon Names of Polygons # of Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 9 10 Nonagon Names of Polygons # of Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Names of Polygons # of Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon Two Types of Polygons Concave: Has at least one corner “pushed in” toward the center Convex: center All corners point away from the Essential Understanding: Perimeter and area are two DIFFERENT ways of measuring geometric figures The perimeter (notated “P”) of a polygon is the sum of the lengths of its sides The area (notated “A”) of a polygon is the number of square units it encloses Many figures have formulas to calculate their perimeter and area. Which do you need to know: area or perimeter? The amount of carpet for the basement floor Area The Perimeter The amount of fence for a dog run amount of paint for the bedroom Area The amount of Halloween lights to hang around the window Perimeter General Formulas Problem 1 want to frame a 5 in by 7 in picture with a 1-inwide frame. What is the perimeter of the picture? What is the perimeter of the outside edge of the frame? 9 in You 5 in 7 in Problem 1 P=2(5 in) + 2(7 in) P=10 in + 14 in Perimeter of the picture is 24 inches 9 in Perimeter of a rectangle has a formula: P=2l + 2w 5 in 7 in Problem 1 P=2(7 in) + 2(9 in) P=14 in + 18 in Perimeter of the picture is 32 inches 9 in Perimeter of a rectangle has a formula: P=2l + 2w 5 in 7 in Circles have special notation and formulas is the notation for circle. The point that represents the center of the circle is listed to the right of the notation How is W read? Circle with center W Circles and Pi The formulas for a circle involve the special number pi (). Pi is the ratio of any circle’s circumference (perimeter) to its diameter. Pi is an irrational number. = 3.1415926… A close approximation is 22 7 Problem 2 What is the circumference and area of the circle at the right? Problem 2 15 inches is the diameter, so we’ll need to use the circumference formula with “d” 𝐶 = 𝜋(𝑑) 𝐶 = 𝜋 15 𝑖𝑛 𝐶 = 15𝜋 𝑖𝑛 This answer is exact Problem 2 15 inches is the diameter, so we’ll need to use the circumference formula with “d” 𝐶 = 𝜋(𝑑) 𝐶 = 𝜋 15 𝑖𝑛 𝐶 = 15𝜋 𝑖𝑛 ≈ 47.1 𝑖𝑛𝑐ℎ𝑒𝑠 This answer is approximate Problem 2 What is the circumference and area of the circle at the right? The area formula needs the radius, which is one-half the diameter 𝑟 = 7.5 𝑖𝑛 Problem 2 What is the circumference and area of the circle at the right? 𝐴 = 𝜋𝑟 2 𝐴 = 𝜋7.52 𝐴 ≈ 176.7 𝑖𝑛2 This is the approximate answer Finding Area of a Rectangle You are designing a poster that will be 3 yd wide and 8 ft high. How much paper do you need to make the poster? Give your answer to the nearest square foot. Your units must be the same. 1 𝑦𝑑 = 3 𝑓𝑡 3 𝑦𝑑 = 9 𝑓𝑡 Finding Area of a Rectangle Use the area for a rectangle formula 𝐴 =𝑙 𝑤 𝐴 = 9 𝑓𝑡 8 𝑓𝑡 𝐴 = 72 𝑓𝑡 2 You need 72 𝑓𝑡 2 of paper to make the poster Your units must be the same. 1 𝑦𝑑 = 3 𝑓𝑡 3 𝑦𝑑 = 9 𝑓𝑡 The units of the floor plan at the right are in feet. Find the perimeter and area of each room. a. the kitchen b. the bedroom c. the bathroom d. the closet