Question
Is this statement true or false? The area of a region is equal to the sum of the areas of the non-overlapping parts. true false
Ask by Nunez Thornton. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The statement is true.
Solution
**True.**
The statement is accurate based on the principle of additivity in geometry. When a region is divided into non-overlapping (disjoint) parts, the total area of the entire region is indeed the sum of the areas of each individual part. This holds true for various geometric shapes and is a fundamental concept in calculating areas.
**Example:**
Consider a rectangle divided into two smaller rectangles without any overlapping. The area of the original rectangle is equal to the sum of the areas of the two smaller rectangles.
\[
\text{Total Area} = \text{Area of Part 1} + \text{Area of Part 2}
\]
This principle ensures that the total area remains consistent regardless of how the region is partitioned, as long as the parts do not overlap.
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Simplify this solution Extra Insights
True! When dealing with areas, if you have a region that can be broken down into non-overlapping parts, the total area of that region is simply the sum of the areas of each part. This principle is foundational in geometry and helps in calculating areas in various contexts, from simple shapes to complex figures. In real-world applications, this concept is hugely beneficial! For example, when planning a garden, you might have different sections for flowers, vegetables, and pathways. By calculating the area of each non-overlapping section and summing them up, you can determine how much space you have for planting or how much soil you need to buy. Planning made easy!
