Geometry 9-5 Changing Dimensions (Non-Proportional) When you change the lengths of the sides of a shape, you change the area and perimeter. When you change just one dimension or when you change two dimensions by different factors, you alter the shape. Halve the base, double the height Multiply the height by 3

Finding Area We can find out how much larger or smaller the areas of the shapes are by using the factors. Ex) double the height of the trapezoid 10 in 8 in 𝑆𝑐𝑎𝑙𝑒 𝐹𝑎𝑐𝑡𝑜𝑟= 𝑁𝑒𝑤 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 8 in 4 in 𝑆𝑐𝑎𝑙𝑒 𝐹𝑎𝑐𝑡𝑜𝑟= 72 36 =2 10 in 𝐴= 1 2 𝑏 1 + 𝑏 2 ℎ 𝐴= 1 2 𝑏 1 + 𝑏 2 ℎ 𝐴= 1 2 8+10 4 =36 𝐴= 1 2 8+10 8 =72

Example Double the base and triple the height. 𝑆𝑐𝑎𝑙𝑒 𝐹𝑎𝑐𝑡𝑜𝑟= 𝑁𝑒𝑤 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 5 in 𝑆𝑐𝑎𝑙𝑒 𝐹𝑎𝑐𝑡𝑜𝑟= 60 10 =6 15 in 4 in 𝐴= 𝑏ℎ 2 𝐴= 𝑏ℎ 2 𝐴= 4∙5 2 =10 𝐴= 8∙15 2 =60 8 in

Shortcut? Is there a shortcut to finding out how the area changes? Ex1) Height doubled Ex2) Height tripled Scale factor:2 Base doubled Scale factor: 6 The effect on the area can be found by multiplying the changes in each dimension.

Example The base is doubled and the height is tripled. The area is…? The length is halved and the width is quadrupled. The area is…? One diagonal is divided by 3, the other diagonal is divided by 4. The area is…? 2 x 3 = multiplied by 6 ½ x 4 = multiplied by 2 1 3 x 1 4 = multiplied by 1 12

Perimeter Does this work for perimeter? No. Unless all dimensions are changed by the same factor. 10 in 4 in 5 in 4 in P=28 P=18 𝑃= 18 28 =.643 𝐴=𝑏ℎ 𝐴=𝑏ℎ 𝐴=10∙4=40 𝐴=5∙4=20 𝐴𝑟𝑒𝑎 𝑆𝑐𝑎𝑙𝑒 𝐹𝑎𝑐𝑡𝑜𝑟= 20 40 = 1 2