1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 5.2 Perimeter

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Know what types of geometric figures are polygons. o Find the perimeters of polygons.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Polygon A polygon is a closed plane figure, with three or more sides, in which each side is a line segment. Each point where two sides meet is called a vertex. Note:A closed figure begins and ends at the same point.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Perimeter The perimeter P of a polygon is the sum of the lengths of its sides.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Formulas for Perimeter Formulas for the Perimeters of Five Polygons

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Finding the Perimeter of a Square Find the perimeter of a square with sides of length 16 inches. Solution Using the formula for the perimeter of a square, we have The perimeter of the square is 64 inches.

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Finding the Perimeter of a Triangle Find the perimeter of a triangle with sides of length 40 mm, 70 mm, and 80 mm. Solution The perimeter of the triangle is 190 mm.

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Finding the Perimeter of a Rectangle Find the perimeter of the rectangle shown. Solution The perimeter of the rectangle is 136 ft.

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Finding the Perimeter of a Polygon Find the perimeter of the polygon shown. (Note: A 5-sided polygon is called a pentagon.)

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Finding the Perimeter of a Polygon (cont.) Solution The perimeter of any polygon is found by adding the lengths of the sides. Thus, for this pentagon we have

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Finding the Cost of a Fencing Project For security, a chain link fence is to be built around a new warehouse building. The property is “L” shaped as shown.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Finding the Cost of a Fencing Project (cont.) a.How many yards of fencing will be needed? b.What will be the cost of the entire fencing project if the price is $12.50 per yard? Solution a.The perimeter of the property is b.The cost will be

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Finding the Perimeter of a Polygon If a rectangle has length 15 ft and width 12 ft, then its perimeter is:

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Finding the Perimeter of a Polygon (cont.) Now, if a small rectangle is cut from one corner of the original rectangle, then a new shape is formed. An interesting fact is that, regardless of the size of the cut out rectangle, this new shape will have the same perimeter as the original rectangle. This is because the length and width of the segments of the new shape are the same as those of the cut out. Note the colored edges.

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Finding the Perimeter of a Polygon (cont.)

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Sketch a figure as an aid for each problem. 1.Find the perimeter of a square with sides of length 15 inches. 2.Find the perimeter of a parallelogram with sides of length 20 m and 25 m. 3.What is the perimeter of a rectangle with width 8 yards and length 12 yards?

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems (cont.) 4.Find the perimeter of the polygon shown:

18. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1.60 inches 2.90 m 3.40 yards 4.46 cm