Percent change in the area of a rectangle

Percent change in the area of a rectangle

If the length of a rectangle is increased by 20% and the width is decreased by 5%, what is the percent change in the area of the rectangle?
Area of a rectangle is length × width.
Convert 20% increase in the length and 5% decrease in the width to decimal and determine the changed area. 
Area before change (100%): 
let length before change  =  𝑙. 
let width before change  =  π‘€.
area  =  π‘™π‘€  = 100%
Area after change:
20% increase of π‘™  =  1 + 0.2𝑙  =  1.2𝑙
5% decrease of π‘€  =  1  0.05𝑀  =  0.95𝑀
area  =  1.2𝑙 × 0.95𝑀  =  1.14𝑙𝑀  =  114%
Determine the change:
114%  100%  =  14%
The area increased by 14%. 
Note that a positive percent change is increase in area and a negative percent change is decrease in area.

If you are not familiar with converting percent increase/decrease to a decimal, follow THIS LINK to read the post.

Try the following:
1.  If the length of a rectangle is increased by 8% and the width is decreased by 15%, what is the percent change in the area of the rectangle?
2.  If the length and the width of a rectangle are each increased by 20%, what is the percent change in the area of the rectangle?
3.  If the length of a rectangle is increased by 25% and the width is decreased by 20%, what is the percent change in the area of the rectangle?

Show/Hide Answers
1.  Changed area is 1.08𝑙 × 0.85𝑀  =  0.918𝑙𝑀  = 91.8%. Percent change in area = 91.8%  100% =   8.2% = 8.2%. (Negative sign indicates 8.2% decrease in area.)
2.  
Changed area is 1.2𝑙 × 1.2𝑀  = 1.44𝑙𝑀  = 144%. Percent change in area = 144%  100% =  44%. (positive sign indicates 44% increase in area.) 
3.  
Changed area is 1.25𝑙 × 0.8𝑀  =  π‘™π‘€  = 100%. Percent change in area = 100%  100% =  0%. (No change in area.)