https://file.aiquickdraw.com/mathbot/file/1729024459608eunix1dr.jpg

To calculate the perimeter of this shape, we need to break it down into simpler components. The shape consists of the following parts:

1. **Straight lines:**
   - Bottom line: 4.00 inches
   - Two vertical sides: 2.00 inches each
   - Two short horizontal sides (at the top corners): 1.00 inch each

2. **Curved sections:**
   - There are two quarter circles, one on each top corner, with a radius of 1.00 inch.

### Steps:
- **Length of the straight lines:**
  The total length of the straight sections is the sum of all the straight lines:
  \[
  4.00 \, \text{in} \, + \, 2(2.00 \, \text{in}) \, + \, 2(1.00 \, \text{in}) = 4.00 \, + \, 4.00 \, + \, 2.00 \, = \, 10.00 \, \text{inches}
  \]

- **Length of the curved sections:**
  Each of the two quarter circles has a radius of 1.00 inch, so the total length of the two quarter-circle arcs combined is the same as the circumference of a single full circle with radius 1.00 inch. The formula for the circumference of a circle is:
  \[
  C = 2\pi r = 2\pi(1.00) \approx 6.2832 \, \text{inches}
  \]
  Since the figure has two quarter-circles, their combined arc length is:
  \[
  \frac{1}{2} \times 6.2832 \approx 3.1416 \, \text{inches}
  \]

### Total Perimeter:
\[
\text{Total Perimeter} = \text{Straight Lines} + \text{Curved Sections} = 10.00 \, \text{inches} \, + 3.1416 \, \text{inches} = 13.1416 \, \text{inches}
\]

Thus, the **perimeter** of the shape is approximately **13.14 inches**.

Would you like further details or have any other questions?

### Follow-up questions:
1. How is the perimeter affected if the radius of the quarter circles changes?
2. Can you calculate the area of the shape?
3. What is the difference between arc length and the perimeter in curved shapes?
4. How would you find the perimeter if the shape had semicircles instead of quarter circles?
5. How would adding a small square cut-out affect the perimeter?

### Tip:
Remember, in composite shapes like this one, breaking the figure into familiar geometric shapes simplifies perimeter and area calculations!

Learn how to calculate the perimeter of a composite figure with straight and curved sides. This problem involves the arc length of quarter circles and straight line segments. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation