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## Columbus State Community College

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**Columbus State Community College**Chapter 3 Section 1 Problem Solving: Perimeter**Problem 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.**Perimeter**Perimeter The distance around the outside edges of any flat shape is called the perimeter of the shape.**Review of a Square**• A square has four sides that are all the same length. • The sides of a square meet to form right angles, which measure 90°. This means that the sides form “square corners.” 5 in. in. is the short way to write inches. In a square, if one right angle is shown, the other three angles are also right angles. The small red square indicates a right angle (90° angle). 5 in. 5 in. 5 in.**Finding the Perimeter of a Square**To find the perimeter of a square, we can “unfold” the shape so the four sides lie end-to-end, as shown below. 7 cm NOTE: cm is the short way to write centimeters. 7 cm 7 cm 7 cm 7 cm 7 cm 7 cm Now we can see the total length of the four sides. The total length is the perimeter of the square. We can find the perimeter by adding. Perimeter = 7 cm + 7 cm + 7 cm + 7 cm = 28 cm or Perimeter = 4 ( 7 cm ) = 28 cm**Perimeter of a Square**Finding the Perimeter of a Square Perimeter of a square = side + side + side + side or P = 4 • side P = 4s**Finding the Perimeter of a Square**EXAMPLE 1 Finding the Perimeter of a Square Find the perimeter of a square that measures 15 yards on each side. Use the formula for perimeter, P = 4s. Formula for perimeter of a square. P = 4 s Replace s with 15 yd. Multiply 4 times 15 yd. P = 4 • 15 yd Write 60 yd; yd is the unit of measure. P = 60 yd The perimeter of the square is 60 yards.**Finding the Length of One Side of a Square**EXAMPLE 2 Finding the Length of One Side of a Square If the perimeter of a square is 36 m, find the length of one side. Formula for perimeter of a square. P = 4 s 36 m = 4 s Replace P with 36 cm 4 s 36 m Divide both sides by 4. = 4 4 9 m = s The length of one side of the square is 9 m.**Review of a Rectangle**• A rectangle has four sides that meet to form right angles (90°). • Each set of opposite sides is parallel and congruent (has the • same length). 90° angles 90° angles**Review of a Rectangle**In a rectangle, if one right angle is shown, the other three angles are also right angles. 21 in. length 7 in. width width 7 in. length 21 in. Perimeter = 21 in.+ 7 in.+ 21 in.+ 7 in. = 56 in.**Finding the Perimeter of a Rectangle**Finding the Perimeter of a Rectangle Perimeter of a rectangle = length + length + width + width or P = ( 2 • length ) + ( 2 • width )P = 2l + 2w**Finding the Perimeter of a Rectangle**EXAMPLE 3 Finding the Perimeter of a Rectangle Find the perimeter of this rectangle. 12 m P = 2 l + 2 w 3 m 3 m P = 2 ( 12 m ) + 2 ( 3 m ) 12 m P = 24 m + 6 m P = 30 m**Finding the Length or Width of a Rectangle**EXAMPLE 4 Finding the Length or Width of a Rectangle If the perimeter of a rectangle is 86 inches and the width is 9 inches, find the length. P = 2 l + 2 w 86 in. = 2 l + 2 ( 9 in. ) ? 86 in. = 2 l + 18 in. 9 in. 9 in. – 18 in. – 18 in. ? 68 in. = 2 l 2 2 34 in. = l The length of the rectangle is 34 inches.**Finding the Length or Width of a Rectangle**EXAMPLE 4 Finding the Length or Width of a Rectangle If 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. + 34 in. + 9 in. + 9 in. 9 in. 9 in. P = 86 in. 34 in. A perimeter of 86 inches matches the information in the original problem, so 34 inches is the correct length of the rectangle.**AD**AB BC DC Parallelograms A parallelogram is a four-sided figure in which opposite sides are both parallel and equal in length. A B is parallel to C D**Finding the Perimeter of a Parallelogram**EXAMPLE 5 Finding the Perimeter of a Parallelogram Find the perimeter of the parallelogram below. 5 yd P = 5 yd + 5 yd + 21 yd + 21 yd 21 yd 21 yd P = 52 yd 5 yd**Finding the Length of a Side of an Irregular Shape**EXAMPLE 6 Finding the Length – Irregular Shapes Find the length of the unlabeled side if the perimeter is 52 feet. 16 ft 4 ft 10 ft ? 9 ft 6 ft 52 ft = 16 ft + 4 ft + x ft + 6 ft + 9 ft + 10 ft 52 ft = x + 45 ft – 45 ft – 45 ft 7 ft = x The length of the unlabeled side is 7 feet.**Problem Solving: Perimeter**Chapter 3 Section 1 – Completed Written by John T. Wallace