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Ch 3 Sec 1: Slide #1 Columbus State Community College Chapter 3 Section 1 Problem Solving: Perimeter

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Ch 3 Sec 1: Slide #2 Problem Solving: Perimeter 1.Use the formula for perimeter of a square to find the perimeter or the length of one side. 2.Use the formula for perimeter of a rectangle to find the perimeter, the length, or the width. 3.Find the perimeter of parallelograms, triangles, and irregular shapes.

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Ch 3 Sec 1: Slide #3 Perimeter The distance around the outside edges of any flat shape is called the perimeter of the shape.

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Ch 3 Sec 1: Slide #4 The small red square indicates a right angle (90° angle). In a square, if one right angle is shown, the other three angles are also right angles. 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.

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Ch 3 Sec 1: Slide #5 NOTE: cm is the short way to write centimeters. 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 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

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Ch 3 Sec 1: Slide #6 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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Ch 3 Sec 1: Slide #7 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 P = 4 15 yd P = 60 yd Formula for perimeter of a square. Replace s with 15 yd. Multiply 4 times 15 yd. Write 60 yd; yd is the unit of measure. The perimeter of the square is 60 yards. EXAMPLE 1 Finding the Perimeter of a Square

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Ch 3 Sec 1: Slide #8 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 36 m = 4 s Formula for perimeter of a square. Replace P with 36 cm Divide both sides by 4. The length of one side of the square is 9 m. 36 m 4 s = 44 9 m = s EXAMPLE 2 Finding the Length of One Side of a Square

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Ch 3 Sec 1: Slide #9 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

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Ch 3 Sec 1: Slide #10 Review of a Rectangle length width 7 in. 21 in. length Perimeter = 21 in. + 7 in in. + 7 in. = 56 in. In a rectangle, if one right angle is shown, the other three angles are also right angles.

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Ch 3 Sec 1: Slide #11 Finding the Perimeter of a Rectangle Perimeter of a rectangle = length + length + width + width or P = ( 2 length ) + ( 2 width ) P = 2l + 2w

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Ch 3 Sec 1: Slide #12 Finding the Perimeter of a Rectangle Find the perimeter of this rectangle. 3 m 12 m P = 2 l + 2 w P = 2 ( 12 m ) + 2 ( 3 m ) P = 24 m + 6 m P = 30 m EXAMPLE 3 Finding the Perimeter of a Rectangle

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Ch 3 Sec 1: Slide #13 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. 9 in. ? ? P = 2 l + 2 w 86 in. = 2 l + 2 ( 9 in. ) 86 in. = 2 l + 18 in. – 18 in. 68 in. = 2 l in. = l The length of the rectangle is 34 inches. EXAMPLE 4 Finding the Length or Width of a Rectangle

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Ch 3 Sec 1: Slide #14 Finding the Length or Width of a Rectangle Check Put the length measurements on your sketch. A perimeter of 86 inches matches the information in the original problem, so 34 inches is the correct length of the rectangle. P = 34 in in. + 9 in. + 9 in. P = 86 in. 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. 9 in. 34 in.

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Ch 3 Sec 1: Slide #15 AD BC Parallelograms A parallelogram is a four-sided figure in which opposite sides are both parallel and equal in length. D C AB AB DC is parallel to

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Ch 3 Sec 1: Slide #16 Finding the Perimeter of a Parallelogram Find the perimeter of the parallelogram below. P = 5 yd + 5 yd + 21 yd + 21 yd P = 52 yd 21 yd 5 yd EXAMPLE 5 Finding the Perimeter of a Parallelogram

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Ch 3 Sec 1: Slide #17 Finding the Length of a Side of an Irregular Shape Find the length of the unlabeled side if the perimeter is 52 feet. 52 ft = 52 ft = x + 45 ft 6 ft 9 ft 10 ft 16 ft ? 4 ft 16 ft +4 ft +x ft +6 ft +9 ft +10 ft EXAMPLE 6 Finding the Length – Irregular Shapes – 45 ft 7 ft = xThe length of the unlabeled side is 7 feet.

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Ch 3 Sec 1: Slide #18 Problem Solving: Perimeter Chapter 3 Section 1 – Completed Written by John T. Wallace

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