https://file.aiquickdraw.com/mathbot/file/1726749244865mhl1gqub.jpg

The image shows a geometric shape composed of a rectangle with two semicircles attached to its shorter sides. The dimensions provided are:

- Length of the rectangle: 60 meters
- Width of the rectangle (equal to the diameter of the semicircles): 40 meters

To find the perimeter and area of this shape, we can break it down into its components:

1. **Perimeter Calculation:**
   - Perimeter of the rectangle portion: \( 2 \times 60 \, \text{m} = 120 \, \text{m} \)
   - Circumference of the two semicircles (which together make a full circle): \( \pi \times 40 \, \text{m} = 125.6 \, \text{m} \)
   - Total perimeter: \( 120 \, \text{m} + 125.6 \, \text{m} = 245.6 \, \text{m} \)

2. **Area Calculation:**
   - Area of the rectangle: \( 60 \, \text{m} \times 40 \, \text{m} = 2400 \, \text{m}^2 \)
   - Area of the full circle formed by the two semicircles: \( \pi \times \left(\frac{40}{2}\right)^2 = \pi \times 20^2 = 1256 \, \text{m}^2 \)
   - Total area: \( 2400 \, \text{m}^2 + 1256 \, \text{m}^2 = 3656 \, \text{m}^2 \)

Would you like more details, or do you have any questions about these calculations?

Here are five related questions for further exploration:

1. What would the perimeter and area be if the rectangle's length increased to 80 meters?
2. How would the results change if the width of the rectangle was reduced to 30 meters?
3. How can we derive the formula for the area of a shape like this in general terms?
4. What is the ratio of the rectangle's area to the semicircles' area?
5. How would the perimeter be affected if only one semicircle were attached?

**Tip:** For composite shapes, always break them down into simpler geometric forms like rectangles, circles, and triangles. This simplifies the calculation process.

Find the perimeter and area of a shape that consists of a rectangle with dimensions 60 meters by 40 meters and two semicircles attached to its shorter sides.

Learn how to calculate the perimeter and area of a composite shape consisting of a rectangle with dimensions of 60 meters by 40 meters and two attached semicircles. Explore step-by-step solutions using key geometry formulas, including the area of a circle and the perimeter of a rectangle. Suitable for students in Grades 9-12.

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