A rectangle has a length of 15 cm and a width of 8 cm. If the length is increased by 20% and the width is decreased by 10%, what is the new area of the rectangle? - Carbonext
Calculating the New Area of a Rectangle After Dimensions Change
Calculating the New Area of a Rectangle After Dimensions Change
Understanding how changes in dimensions affect the area of a rectangle is essential in geometry, architecture, and real-world design. Take this practical example: a rectangle with an initial length of 15 cm and a width of 8 cm. If the length is increased by 20% and the width is reduced by 10%, what is the new area? Let’s break it down step by step.
Understanding the Context
Original Dimensions
- Length (l): 15 cm
- Width (w): 8 cm
The original area is calculated as:
Area = Length × Width = 15 × 8 = 120 cm²
Key Insights
Applying the Percentage Changes
1. Increase the length by 20%:
A 20% increase means multiplying the length by 1.20:
New length = 15 cm × 1.20 = 18 cm
2. Decrease the width by 10%:
A 10% decrease means multiplying the width by 0.90:
New width = 8 cm × 0.90 = 7.2 cm
Calculating the New Area
🔗 Related Articles You Might Like:
You’ll Never Guess What Happens In Fifty Days From Today Inside 50 Days That Rewrite Your Life Forever The Shocking Truth Revealed in Just 50 DaysFinal Thoughts
Now, multiply the updated dimensions:
New Area = New Length × New Width = 18 × 7.2 = 129.6 cm²
Final Answer
After adjusting the dimensions—length increased by 20% (15 cm → 18 cm) and width decreased by 10% (8 cm → 7.2 cm)—the rectangle’s new area is 129.6 square centimeters.
Understanding these transformations helps in practical applications such as material estimation, space planning, and design optimization. Whether you’re constructing a physical structure or working with digital blueprints, mastering area calculations ensures precision and efficiency.
Keywords: rectangle area calculation, length increase 20%, width decrease 10%, geometry problems, area change, 15 cm rectangle, 8 cm rectangle, how to calculate new area, real-world math applications
For more tips on geometry and measurement transformations, explore our comprehensive guides on calculating areas and resizing shapes.
