Lesson 4.5 Core Focus on Decimals & Fractions Perimeter with Fractions Warm-Up 1. Simplify 1 164 inches . 1 14 inches 2. 3 12 2 34 6 14 3 3. 4 18 3 16 7 165 15 4. 8 14 6 16 15 163 Lesson 4.5 Perimeter with Fractions Add lengths, including fractions and mixed numbers, of the sides of polygons to find perimeters. Vocabulary Perimeter The distance around a closed figure. Polygon A closed figure formed by three or more line segments. Finding Perimeter 1. Measure all sides (if necessary). 2. Add the lengths of all sides together. Example 1 Find the perimeter of the rectangle in inches. Use a ruler to measure each side of the shape to the nearest sixteenth of an inch. 3 Length = in 4 Add all sides. Simplify. The perimeter is 2 inches. 12 3 16 4 1 Width = in 4 3 1 3 1 8 2 4 4 4 4 4 Opposite sides of rectangles are the same length. 4 1 16 4 Example 2 Use the given measurements to find the perimeter of the polygon. Add the lengths of all sides together. 1 18 5 5 5 5 1 18 16 16 16 16 Change the mixed numbers to improper fractions. 1 18 9 8 Use the LCD to rename the fractions. The LCD is 16. 9 18 8 16 Add the sides of the polygon. 18 5 5 18 5 5 56 16 16 16 16 16 16 16 Simplify. 56 7 3 12 16 2 The perimeter of the polygon is 3 12 inches. Example 3 Brayden went for a walk. He walked in a rectangular pattern around a city block. First he walked 66 23 yards. He turned right and walked 76 16 yards. He turned right two more times and ended up where he started. What was the perimeter of the city block? Brayden walked in a rectangular pattern. Add the four sides. 66 23 76 16 66 32 76 16 ? yards 66 23 66 64 Use the LCD to rename the fractions. The LCD is 6. Add the sides of the city block. 66 64 76 16 66 64 76 16 284 106 Simplify. 10 1 64 284 1 64 285 64 285 23 6 The perimeter of the city block Brayden walked was 285 23 yards. Example 4 Use the given measurement to find the perimeter of the square. Add all four sides of the square together. 1 12 1 12 1 12 1 12 4 42 All sides of a square are the same length. Simplify. 4 42 4 2 6 The perimeter of the square is 6 inches. Communication Prompt Why should you know how to find the perimeter of an object? Exit Problems 1. What is the perimeter of a rectangle that is 2 85 inches long and 1 12 inches wide? 8 14 inches 2. What is the perimeter of a triangle with sides that measure: 3 14 inches, 4 12 inches and 5 12 inches? 13 14 inches 3. What is the perimeter of a square with a side that measures 7 inch? 8 3 12 inches