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**Columbus State Community College**

Chapter 3 Section 1 Problem Solving: Perimeter

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**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.

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Perimeter Perimeter The distance around the outside edges of any flat shape is called the perimeter of the shape.

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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.

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**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 cm cm cm = 28 cm or Perimeter = 4 ( 7 cm ) = 28 cm

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Perimeter of a Square Finding the Perimeter of a Square Perimeter of a square = side side side side or P = 4 • side P = 4s

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**Finding the Perimeter of a Square**

EXAMPLE 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. P = 4 s Formula for perimeter of a square. P = 4 • 15 yd Replace s with 15 yd. Multiply 4 times 15 yd. P = 60 yd Write 60 yd; yd is the unit of measure. The perimeter of the square is 60 yards.

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**Finding the Length of One Side of a Square**

EXAMPLE Finding the Length of One Side of a Square If the perimeter of a square is 36 m, find the length of one side. P = 4 s Formula for perimeter of a square. 36 m = 4 s Replace P with 36 cm 36 m 4 s Divide both sides by 4. = 4 4 9 m = s The length of one side of the square is 9 m.

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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

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**Perimeter = 21 in. + 7 in. + 21 in. + 7 in. = 56 in.**

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 in in in. = 56 in.

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**Finding the Perimeter of a Rectangle**

Perimeter of a rectangle = length length width width or P = ( 2 • length ) ( 2 • width ) P = l w

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**Finding the Perimeter of a Rectangle**

EXAMPLE Finding the Perimeter of a Rectangle Find the perimeter of this rectangle. 12 m P = 2 l w 3 m 3 m P = 2 ( 12 m ) ( 3 m ) 12 m P = m m P = m

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**Finding the Length or Width of a Rectangle**

EXAMPLE 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 w 86 in. = 2 l ( 9 in. ) ? 86 in. = 2 l 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.

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**Finding the Length or Width of a Rectangle**

EXAMPLE 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 in in 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.

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Parallelograms A parallelogram is a four-sided figure in which opposite sides are both parallel and equal in length. A B AD AB is parallel to BC DC D C

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**Finding the Perimeter of a Parallelogram**

EXAMPLE Finding the Perimeter of a Parallelogram Find the perimeter of the parallelogram below. 5 yd P = 5 yd yd yd yd 21 yd 21 yd P = 52 yd 5 yd

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**Finding the Length of a Side of an Irregular Shape**

EXAMPLE 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 ft – 45 ft – 45 ft 7 ft = x The length of the unlabeled side is 7 feet.

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**Problem Solving: Perimeter**

Chapter 3 Section 1 – Completed Written by John T. Wallace

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