Area Of A Shaded Part Of Rectangle

✏️ Worked Example - Find Area of Shaded Region

🧠 Math Vocabulary

• Shaded region: The portion of a figure whose area is being measured.
• Composite figure: A figure formed by combining or overlapping simpler shapes.
• Radius: A segment from the center of a circle to a point on the circle.
• Diameter: A segment through the center of a circle with endpoints on the circle; it equals twice the radius.
• Rectangle: A quadrilateral with four right angles.
• Area: The amount of two-dimensional space inside a figure.
• Subtract: To remove one quantity from another.
• Congruent circles: Circles with equal radii and equal diameters.
• Square unit: A unit used to measure area, such as a square inch.

💡 Main Idea

To find the shaded area surrounding the two circles, first calculate the area of the entire rectangle. Next, find the radius and area of each circle. Add the two circle areas and subtract that amount from the rectangle’s area. The remaining difference is the shaded region.

📚 What You Should Already Know

You should know how to find rectangle area using \(A=lw\) and circle area using \(A=\pi r^2\). You should also understand that the diameter is twice the radius and recognize when subtraction is needed to remove an unshaded portion from a larger region.

🚀 What Comes Next

Next, students can solve shaded-region problems involving semicircles, quarter circles, overlapping circles, and circular regions inside squares or other polygons. These strategies also support composite-area and real-world design problems.

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