Introduction to Area of Shaded Region
Calculating the area of shaded regions is a fundamental concept in geometry and mathematics. It involves finding the area of a specific portion of a shape or figure that is shaded or highlighted. In this article, we will explore the concept of area of shaded regions, provide examples, and offer a worksheet with answers to help you practice.
Understanding the Concept of Area of Shaded Region
The area of a shaded region is the total area of the shaded portion of a shape or figure. It can be calculated by finding the area of the entire shape and then subtracting the area of the unshaded portion.
Key Concepts:
- Shape: A self-contained area with a defined boundary.
- Shaded Region: A portion of a shape that is highlighted or shaded.
- Area: The total size of a shape or region.
Calculating the Area of Shaded Region
To calculate the area of a shaded region, follow these steps:
- Identify the shape and the shaded region.
- Find the area of the entire shape.
- Find the area of the unshaded portion.
- Subtract the area of the unshaded portion from the area of the entire shape.
Formula: Area of Shaded Region = Area of Entire Shape - Area of Unshaded Portion
Examples and Solutions
Example 1: Find the area of the shaded region in the rectangle below.
Rectangle with a shaded region
Solution:
Area of Entire Shape (Rectangle) = Length × Width = 6 × 4 = 24 Area of Unshaded Portion (Triangle) = (1⁄2) × Base × Height = (1⁄2) × 3 × 4 = 6 Area of Shaded Region = Area of Entire Shape - Area of Unshaded Portion = 24 - 6 = 18
Example 2: Find the area of the shaded region in the circle below.
Circle with a shaded region
Solution:
Area of Entire Shape (Circle) = π × Radius^2 = 3.14 × 4^2 = 50.24 Area of Unshaded Portion (Triangle) = (1⁄2) × Base × Height = (1⁄2) × 4 × 4 = 8 Area of Shaded Region = Area of Entire Shape - Area of Unshaded Portion = 50.24 - 8 = 42.24
Worksheet with Answers
Try the following worksheet to practice calculating the area of shaded regions:
| Shape | Shaded Region | Area of Entire Shape | Area of Unshaded Portion | Area of Shaded Region |
|---|---|---|---|---|
| Rectangle | 12 × 8 = 96 | (1⁄2) × 4 × 6 = 12 | 96 - 12 = 84 | |
| Triangle | (1⁄2) × 10 × 12 = 60 | 4 × 6 = 24 | 60 - 24 = 36 | |
| Circle | 3.14 × 6^2 = 113.04 | (1⁄2) × 6 × 6 = 18 | 113.04 - 18 = 95.04 |
Answers:
- 84
- 36
- 95.04
Conclusion
Calculating the area of shaded regions is an essential concept in geometry and mathematics. By understanding the concept and practicing with examples, you can become proficient in finding the area of shaded regions. Remember to use the formula: Area of Shaded Region = Area of Entire Shape - Area of Unshaded Portion.
What is the area of a shaded region?
+The area of a shaded region is the total area of the shaded portion of a shape or figure.
How do I calculate the area of a shaded region?
+To calculate the area of a shaded region, find the area of the entire shape, find the area of the unshaded portion, and subtract the area of the unshaded portion from the area of the entire shape.
What is the formula for calculating the area of a shaded region?
+Area of Shaded Region = Area of Entire Shape - Area of Unshaded Portion
