Chapter 1 - XYZ Custom Plus

1.2 Addition with Whole Numbers, and Perimeter19EPerimeterfacts from geometry PerimeterWe end this section with an introduction to perimeter. Here we will find theperimeter of several different shapes called polygons. A polygon is a closedgeometric figure, with at least three sides, in which each side is a straight linesegment.The most common polygons are squares, rectangles, and triangles.Examples of these are shown in Figure 2.squarerectangletrianglewhslbFigure 2NoteIn the triangle, thesmall square wherethe broken line meetsthe base is the notation we use toshow that the two line segmentsmeet at right angles. That is, theheight h and the base b are perpendicularto each other; the anglebetween them is 90°.In the square, s is the length of the side, and each side has the same length.In the rectangle, l stands for the length, and w stands for the width. Thewidth is usually the lesser of the two. The b and h in the triangle are the baseand height, respectively. The height is always perpendicular to the base. Thatis, the height and base form a 90°, or right, angle where they meet.DefinitionThe perimeter of any polygon is the sum of the lengths of the sides, and itis denoted with the letter P.Example 9Find the perimeter of each geometric figure.a. b. c.36 yards24 feet23 yards9. Find the perimeter of each geometricfigure.a.15 inches37 feet24 yards24 yards7 feet12 yardsb.Solution In each case we find the perimeter by adding the lengths of all thesides.a. The figure is a square. Because the length of each side in thesquare is the same, the perimeter isP = 15 + 15 + 15 + 15 = 60 inchesc.88 inches44 yards33 inches66 yardsb. In the rectangle, two of the sides are 24 feet long, and the othertwo are 37 feet long. The perimeter is the sum of the lengths ofthe sides.77 yardsP = 24 + 24 + 37 + 37 = 122 feetc. For this polygon, we add the lengths of the sides together. Theresult is the perimeter.P = 36 + 23 + 24 + 12 + 24 = 119 yardsAnswer9. a. 28 feet b. 242 inchesc. 187 yards