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### 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  =  𝑤.
area  =  𝑙𝑤  = 100%
Area after change:
20% increase of 𝑙  =  1 ＋ 0.2𝑙  =  1.2𝑙
5% decrease of 𝑤  =  1  0.05𝑤  =  0.95𝑤
area  =  1.2𝑙 × 0.95𝑤  =  1.14𝑙𝑤  =  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?