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. 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.

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. 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.

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

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. + 7 in. + 21 in. + 7 in. = 56 in.

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.

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

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