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Find the area of the shaded region.
Published on October 19, 2024
Geometry
To find the area of the shaded region, subtract the area of a circle (formed by two semicircles) from the area of the enclosing rectangle.
Question
Find the Area of the Shaded Region
Answer
Let’s break down how to find the area of the shaded region:
1. Recognize the Shapes
- We have a rectangle as the outer shape.
- We have two semicircles within the rectangle.
2. Semicircles Make a Circle
- Notice that the two semicircles, when put together, form a complete circle.
3. The Plan
- We’ll find the area of the rectangle.
- We’ll find the area of the circle.
- We’ll subtract the circle’s area from the rectangle’s area to get the shaded region’s area.
4. Area of the Rectangle
- Area of a rectangle = length * width
- Length = 24cm
- Width = 14cm
- Area of rectangle = 24cm * 14cm = 336 cm²
5. Area of the Circle
- Area of a circle = π * radius²
- The diameter of the circle is equal to the width of the rectangle (14cm).
- Radius = diameter / 2 = 14cm / 2 = 7cm
- Area of circle = π * (7cm)² = 49π cm²
6. Area of the Shaded Region
- Area of shaded region = Area of rectangle - Area of circle
- Area of shaded region = 336 cm² - 49π cm²
Answer: The area of the shaded region is (336 - 49π) cm².