Find the perimeter and area of the polygon shown below.

To find the perimeter and area of the given trapezoid that consists of a rectangle and a right triangle, we'll first determine the dimensions and then apply the appropriate formulas.

### Given Dimensions:
- **Rectangle**:
- Length (base of trapezoid) = 20 feet
- Width = 15 feet

- **Right Triangle**:
- Height = 15 feet (this is the same as the width of the rectangle)
- Base = 8 feet
- Hypotenuse = 17 feet

### Area Calculation:

1. **Area of the Rectangle**:
\[
\text{Area}_{rectangle} = \text{length} \times \text{width} = 20 \, \text{ft} \times 15 \, \text{ft} = 300 \, \text{square feet}
\]

2. **Area of the Triangle**:
\[
\text{Area}_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \, \text{ft} \times 15 \, \text{ft} = \frac{1}{2} \times 120 \, \text{square feet} = 60 \, \text{square feet}
\]

3. **Total Area of the Trapezoid**:
\[
\text{Area}_{trapezoid} = \text{Area}_{rectangle} + \text{Area}_{triangle} = 300 \, \text{square feet} + 60 \, \text{square feet} = 360 \, \text{square feet}
\]

### Perimeter Calculation:

The perimeter of the trapezoid consists of the lengths of all the sides:

1. **Sides of the Polygon**:
- Bottom side (rectangle) = 20 feet
- Left side (height of the rectangle) = 15 feet
- Right side (triangle) = hypotenuse = 17 feet
- Base of the triangle = 8 feet

2. **Calculate the Pairs** (Other side of the rectangle is also 15 feet):
\[
\text{Perimeter} = \text{bottom} + \text{left} + \text{hypotenuse} + \text{base} = 20 \, \text{ft} + 15 \, \text{ft} + 17 \, \text{ft} + 8 \, \text{ft}
\]

Adding those:
\[
\text{Perimeter} = 20 + 15 + 17 + 8 = 60 \, \text{feet}
\]

### Final Results:
- **Area**: 360 square feet
- **Perimeter**: 60 feet

Therefore, the area of the trapezoid is **360 square feet**, and the perimeter is **60 feet**.