https://file.aiquickdraw.com/mathbot/file/1727405038655bbkkazje.jpg

The image shows a polygon with labeled side lengths, and you're asked to find the perimeter and area. Let’s break it down:

### Perimeter Calculation
The polygon has 5 sides with the following lengths:
- One horizontal side: \( 20 \, \text{ft} \)
- One vertical side: \( 15 \, \text{ft} \)
- One diagonal side: \( 17 \, \text{ft} \)
- One horizontal side: \( 8 \, \text{ft} \)
- The final vertical side: This corresponds to the height of the trapezoid and is equal to \( 15 \, \text{ft} \) since it’s a rectangle on the left.

Thus, the perimeter \( P \) is:
\[
P = 20 + 15 + 17 + 8 = 60 \, \text{ft}
\]

### Area Calculation
The polygon appears to be a combination of a rectangle and a right triangle.
- **Rectangle Area**: 
  \[
  A_{\text{rect}} = 20 \times 15 = 300 \, \text{sq ft}
  \]
  
- **Right Triangle Area**: 
  The right triangle has a base of \( 8 \, \text{ft} \) and a height of \( 15 \, \text{ft} \). So, its area is:
  \[
  A_{\text{tri}} = \frac{1}{2} \times 8 \times 15 = 60 \, \text{sq ft}
  \]

Thus, the total area \( A \) is:
\[
A = 300 + 60 = 360 \, \text{sq ft}
\]

### Conclusion:
The correct option is:
\[
P = 60 \, \text{ft}, \, A = 360 \, \text{sq ft}
\]

Do you have any questions or would you like further details?

Here are some related questions for practice:
1. How do you calculate the perimeter of irregular polygons?
2. What is the general formula for the area of a right triangle?
3. How can you apply the Pythagorean theorem to verify the length of the diagonal?
4. How do you decompose complex shapes to calculate area?
5. How does changing one side length affect the area and perimeter?

**Tip**: Decomposing complex shapes into simpler ones (rectangles, triangles) is a powerful tool for solving area problems.

Find the perimeter and area of the polygon shown below.

Learn how to find the perimeter and area of a polygon shaped like a trapezoid and a right triangle. This detailed solution breaks down the calculation steps and uses key geometric formulas. Suitable for Grades 7-9 students.

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