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 = π.**

**let width before change = π€.**

**area = ππ€ =**

**100%**

**Area after change:**

**20% increase of π = 1 ＋ 0.2π = 1.2π**

**5% decrease of π€ = 1**

**−**

**0.05π€ = 0.95π€**

**area = 1.2π × 0.95π€ = 1.14ππ€ =**

**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 1.08π × 0.85π€ = 0.918ππ€ = 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 1.2π × 1.2π€ = 1.44ππ€ = 144%. Percent change in area = 144% − 100% = 44%. (positive sign indicates 44% increase in area.)

3. Changed area is 1.25π × 0.8π€ = ππ€ = 100%. Percent change in area = 100% − 100% = 0%. (No change in area.)

2. Changed area is 1.2π × 1.2π€ = 1.44ππ€ = 144%. Percent change in area = 144% − 100% = 44%. (positive sign indicates 44% increase in area.)

3. Changed area is 1.25π × 0.8π€ = ππ€ = 100%. Percent change in area = 100% − 100% = 0%. (No change in area.)