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Let's break down the problem:

We have a rectangular piece of paper with dimensions 24 cm (length) and 16 cm (width), with a semicircle cut out from one side (the shorter side). The objective is to find:

1. **The perimeter of the paper** after the semicircle is cut out.
2. **The area of the paper** after the semicircle is cut out.

### Part a) Finding the Perimeter

- The perimeter of the rectangle without the cutout would normally be:
  \[
  \text{Perimeter of rectangle} = 2(\text{length} + \text{width}) = 2(24 + 16) = 80 \, \text{cm}
  \]
  
- Since a semicircle is cut out, we need to subtract the width of the rectangle that matches the diameter of the semicircle and add the circumference of the semicircle.

- The diameter of the semicircle is 16 cm (the width of the rectangle), so the radius \( r \) is:
  \[
  r = \frac{16}{2} = 8 \, \text{cm}
  \]

- The circumference of a full circle is \( 2\pi r \), so the circumference of the semicircle is:
  \[
  \text{Circumference of semicircle} = \pi r = 3.14 \times 8 = 25.12 \, \text{cm}
  \]

- The modified perimeter will be:
  \[
  \text{Perimeter} = 80 \, \text{cm (original)} - 16 \, \text{cm (width)} + 25.12 \, \text{cm (semicircle circumference)} = 89.12 \, \text{cm}
  \]

### Part b) Finding the Area

- The area of the rectangle is:
  \[
  \text{Area of rectangle} = \text{length} \times \text{width} = 24 \times 16 = 384 \, \text{cm}^2
  \]

- The area of the semicircle is half the area of a full circle:
  \[
  \text{Area of semicircle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times 8^2 = \frac{1}{2} \times 3.14 \times 64 = 100.48 \, \text{cm}^2
  \]

- The modified area will be:
  \[
  \text{Area} = 384 \, \text{cm}^2 - 100.48 \, \text{cm}^2 = 283.52 \, \text{cm}^2
  \]

### Final Answers:
- **Perimeter** = 89.12 cm
- **Area** = 283.52 cm²

Let me know if you would like any further clarification or additional details.

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Here are 5 related questions you might want to explore:
1. How would the perimeter change if the semicircle had a different radius?
2. What is the perimeter if the shape had a full circle instead of a semicircle cut out?
3. How do the area and perimeter change if the dimensions of the rectangle increase proportionally?
4. What if the cutout was an equilateral triangle instead of a semicircle?
5. How would you calculate the perimeter and area if an ellipse was cut out instead of a semicircle?

**Tip**: Remember, when dealing with circles, always ensure you use the correct approximation for \(\pi\) depending on the precision required (e.g., 3.14, or \(\pi\) in exact terms).

A rectangular piece of paper with a length of 24 centimeters and a width of 16 centimeters has a semicircle cut out of it. Find the perimeter and area of the remaining shape.

Learn how to calculate the perimeter and area of a rectangle with a semicircle cut out from one side. This problem involves key geometric concepts like perimeter and area calculations for composite shapes, using formulas for rectangles and semicircles. Suitable for students in Grades 6-8.

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