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? - Coaching Toolbox
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
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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
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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.
