https://file.aiquickdraw.com/mathbot/file/1726592360061gkgbqztp.jpg

To find the perimeter of this composite figure, which consists of a parallelogram and two semicircles, follow these steps:

1. **Identify the lengths:**
   - The length of the longer side of the parallelogram (the distance between the centers of the two semicircles) is given as 9 units.
   - The shorter side of the parallelogram (which is also the diameter of each semicircle) is given as 4 units. Therefore, the radius of each semicircle is \( \frac{4}{2} = 2 \) units.

2. **Calculate the perimeter of the semicircles:**
   - Since the figure has two semicircles, together they form a full circle with a radius of 2.
   - The circumference of a full circle is given by the formula \( 2\pi r \).
   - Using the radius \( r = 2 \), the circumference of the circle is:
     \[
     2\pi \times 2 = 4\pi
     \]

3. **Calculate the perimeter of the parallelogram:**
   - The total perimeter of the parallelogram includes the two lengths that contribute to the perimeter: the longer side (length 9) and the two shorter segments. Since the semicircles sit on these shorter sides, they don't contribute to the total perimeter directly, so we only need the top and bottom:
     - Top side: 9 units
     - Bottom side: 9 units
   - Together, the sum of these two sides is:
     \[
     9 + 9 = 18
     \]

4. **Combine the perimeter components:**
   - Add the perimeter of the full circle (formed by the two semicircles) and the total length of the parallelogram:
     \[
     4\pi + 18
     \]
   - Plug in \( \pi \approx 3.14 \):
     \[
     4 \times 3.14 + 18 = 12.56 + 18 = 30.56
     \]

5. **Round to the nearest tenth:**  
   The perimeter is approximately **30.6 units**.

Would you like a detailed explanation of any part of this solution, or do you have any questions?

Here are 5 related questions to expand upon this problem:
1. How do you find the area of a composite figure like this one?
2. What is the formula for the circumference of a circle, and how does it change for semicircles?
3. How would the perimeter change if the radii of the semicircles were different?
4. How do you find the area of a parallelogram?
5. What if the figure were composed of quarter circles instead of semicircles? How would you find the perimeter?

**Tip:** When dealing with composite figures, break the figure into simpler shapes (like circles, triangles, and rectangles) to find the perimeter or area more easily.

Find the perimeter of the figure below, composed of a parallelogram and two semicircles. Round to the nearest tenths place.

Learn how to find the perimeter of a composite figure that consists of a parallelogram and two semicircles. This problem includes key concepts in geometry, such as calculating the circumference of a semicircle and applying it to composite shapes. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation