Mathematics - PearsonAccess.com

Objective 8The actual width of the bedroom is 15 feet.A 20 • 15A 300 ft 2It will take 300 square feet of carpet to cover the bedroom floor.How Does a Dilation Affect the Perimeter, Area, and Volume of aFigure?When the dimensions of a figure are dilated by a scale factor:● The perimeter of the dilated figure is changed by the samescale factor.For example, if the dimensions were increased by a factor of 3,then the perimeter would increase by a factor of 3.If the dimensions of two similar figures are in the ratio a b ,then their perimeters are also in the ratio a b .● The area of the dilated figure is changed by the square of thescale factor.For example, if the dimensions were reduced by a factor of 1 2 ,●then the area would be reduced by a factor of ( 1 2 ) 2 , or 1 4 .If the dimensions of two similar figures are in the ratio a b ,then their areas are in the ratio ( a b ) 2 a 2b 2.The volume of the dilated figure is changed by the cube of thescale factor.For example, if the dimensions were increased by a factor of 2,then the volume would increase by a factor of 2 3 , or 8.If the dimensions of two similar solid figures are in the33.ratio a b , then their volumes are in the ratio ( a b ) 3 a bA hexagon with a perimeter of 54 centimeters is dilated by a scalefactor of 1 . What is the perimeter of the dilated hexagon?4The perimeter of the dilated figure will change by a scale factor of 1 4 .To find the perimeter of the dilated hexagon, multiply theperimeter of the original hexagon by the scale factor, 1 4 .54 • 1 4 13.5The perimeter of the dilated hexagon is 13.5 centimeters.219