Presentation on theme: "Columbus State Community College"— Presentation transcript:
1Columbus State Community College Chapter 3 Section 1Problem Solving: Perimeter
2Problem Solving: Perimeter Use the formula for perimeter of a square to find the perimeter or the length of one side.Use the formula for perimeter of a rectangle to find the perimeter, the length, or the width.Find the perimeter of parallelograms, triangles, and irregular shapes.
3PerimeterPerimeterThe distance around the outside edges of any flat shape is called the perimeter of the shape.
4Review of a SquareA square has four sides that are all the same length.The sides of a square meet to form right angles, whichmeasure 90°. This means that the sides form “square corners.”5 in.in. is the short wayto write inches.In a square, if one rightangle is shown, theother three angles arealso right angles.The small red squareindicates a right angle(90° angle).5 in.5 in.5 in.
5Finding the Perimeter of a Square To find the perimeter of a square, we can “unfold” the shape so thefour sides lie end-to-end, as shown below.7 cmNOTE: cm is the short way towrite centimeters.7 cm7 cm7 cm7 cm7 cm7 cmNow we can see the total length of the four sides. The total length isthe perimeter of the square. We can find the perimeter by adding.Perimeter = 7 cm cm cm cm = 28 cmorPerimeter = 4 ( 7 cm ) = 28 cm
6Perimeter of a SquareFinding the Perimeter of a SquarePerimeter of a square = side side side sideor P = 4 • sideP = 4s
7Finding the Perimeter of a Square EXAMPLE Finding the Perimeter of a SquareFind the perimeter of a square that measures 15 yards on each side.Use the formula for perimeter, P = 4s.P = 4 sFormula for perimeter of a square.P = 4 • 15 ydReplace s with 15 yd. Multiply 4 times 15 yd.P = 60 ydWrite 60 yd; yd is the unit of measure.The perimeter of the square is 60 yards.
8Finding the Length of One Side of a Square EXAMPLE Finding the Length of One Side of a SquareIf the perimeter of a square is 36 m, find the length of one side.P = 4 sFormula for perimeter of a square.36 m = 4 sReplace P with 36 cm36 m4 sDivide both sides by 4.=449 m = sThe length of one side of the square is 9 m.
9Review of a RectangleA rectangle has four sides that meet to form right angles (90°).Each set of opposite sides is parallel and congruent (has thesame length).90° angles90° angles
10Perimeter = 21 in. + 7 in. + 21 in. + 7 in. = 56 in. Review of a RectangleIn a rectangle, if one right angle is shown,the other three angles are also right angles.21 in.length7 in.widthwidth7 in.length21 in.Perimeter = 21 in in in in. = 56 in.
11Finding the Perimeter of a Rectangle Perimeter of a rectangle = length length width widthor P = ( 2 • length ) ( 2 • width ) P = l w
12Finding the Perimeter of a Rectangle EXAMPLE Finding the Perimeter of a RectangleFind the perimeter of this rectangle.12 mP = 2 l w3 m3 mP = 2 ( 12 m ) ( 3 m )12 mP = m mP = m
13Finding the Length or Width of a Rectangle EXAMPLE Finding the Length or Width of a RectangleIf the perimeter of a rectangle is 86 inches and the width is 9 inches,find the length.P = 2 l w86 in. = 2 l ( 9 in. )?86 in. = 2 l in.9 in.9 in.– 18 in.– 18 in.?68 in. = 2 l2234 in. = lThe length of the rectangle is 34 inches.
14Finding the Length or Width of a Rectangle EXAMPLE Finding the Length or Width of a RectangleIf the perimeter of a rectangle is 86 inches and the width is 9 inches,find the length.Check Put the length measurements on your sketch.34 in.P = 34 in in in in.9 in.9 in.P = 86 in.34 in.A perimeter of 86 inches matches the information in the originalproblem, so 34 inches is the correct length of the rectangle.
15ParallelogramsA parallelogram is a four-sided figure in which opposite sides areboth parallel and equal in length.ABADABis parallel toBCDCDC
16Finding the Perimeter of a Parallelogram EXAMPLE Finding the Perimeter of a ParallelogramFind the perimeter of the parallelogram below.5 ydP = 5 yd yd yd yd21 yd21 ydP = 52 yd5 yd
17Finding the Length of a Side of an Irregular Shape EXAMPLE Finding the Length – Irregular ShapesFind the length of the unlabeled side if the perimeter is 52 feet.16 ft4 ft10 ft?9 ft6 ft52 ft =16 ft +4 ft +x ft +6 ft +9 ft +10 ft52 ft = x ft– 45 ft– 45 ft7 ft = x The length of the unlabeled side is 7 feet.
18Problem Solving: Perimeter Chapter 3 Section 1 – CompletedWritten by John T. Wallace