https://file.aiquickdraw.com/mathbot/file/172568345392212l5w9oi.jpg

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Based on the image, the task involves finding the perimeter and area of a trapezoid. Here's how to approach it:

### Given:
- The trapezoid has the following dimensions:
  - Top base: 12.79 units
  - Bottom base: 30.15 units
  - Left slant side: 20.63 units
  - Right slant side: 21.87 units
  - Height: 14.90 units

### 1. **Perimeter Calculation**:
The perimeter \( P \) of a trapezoid is the sum of the lengths of all four sides:
\[
P = \text{top base} + \text{bottom base} + \text{left slant side} + \text{right slant side}
\]
Substituting the given values:
\[
P = 12.79 + 30.15 + 20.63 + 21.87 = 85.44 \text{ units}
\]

### 2. **Area Calculation**:
The area \( A \) of a trapezoid is given by the formula:
\[
A = \frac{1}{2} \times (\text{top base} + \text{bottom base}) \times \text{height}
\]
Substituting the given values:
\[
A = \frac{1}{2} \times (12.79 + 30.15) \times 14.90
\]
\[
A = \frac{1}{2} \times 42.94 \times 14.90
\]
\[
A = 319.81 \text{ square units}
\]

Thus, the **perimeter** is approximately **85.44 units**, and the **area** is approximately **319.81 square units**.

Would you like further details or a more in-depth explanation of any part? Here are some related questions:

1. How do we calculate the height of a trapezoid if it's not given?
2. Can the slant heights be used directly in area calculation?
3. How does the formula for the area of a trapezoid differ from that of a triangle?
4. Why is the sum of the bases important in finding the area?
5. What is the significance of rounding to hundredths?

**Tip:** Always check that all sides are in the same units before calculating the perimeter or area.

Find the perimeter and area of the trapezoid shown in the diagram. Round your answer to the nearest hundredth as needed.

Learn how to calculate the perimeter and area of a trapezoid using given side lengths and height. This solution demonstrates the step-by-step process, including formulas for perimeter and area, with rounding to the nearest hundredth. Suitable for students in Grades 8-10.

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