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The question asks to determine (a) the area and (b) the perimeter of a quadrilateral, and a diagram of a parallelogram is provided with the following measurements:

- The base of the parallelogram is \( 19 \, \text{in} \),
- The height of the parallelogram is \( 4 \, \text{in} \),
- The side length (slant height) is \( 9 \, \text{in} \).

### (a) Area of the Parallelogram
The area \( A \) of a parallelogram is given by the formula:
\[
A = \text{base} \times \text{height}
\]
Substituting the known values:
\[
A = 19 \, \text{in} \times 4 \, \text{in} = 76 \, \text{square inches}
\]

### (b) Perimeter of the Parallelogram
The perimeter \( P \) of a parallelogram is the sum of all its sides. Since a parallelogram has two pairs of equal sides, the perimeter is:
\[
P = 2 \times (\text{base} + \text{side})
\]
Substituting the given values:
\[
P = 2 \times (19 \, \text{in} + 9 \, \text{in}) = 2 \times 28 \, \text{in} = 56 \, \text{in}
\]

### Final answers:
- **The area of the parallelogram is 76 square inches.**
- **The perimeter of the parallelogram is 56 inches.**

Would you like more detailed steps or any clarification on the formulas? 

Here are 5 related questions:
1. What is the formula for the area of a trapezoid, and how does it differ from a parallelogram?
2. How do you calculate the perimeter of irregular quadrilaterals?
3. What is the difference between the height and the slant height in various shapes?
4. How do you find the area of a quadrilateral if it's not a parallelogram?
5. How can you calculate the area of a rhombus using its diagonals?

**Tip:** When working with parallelograms, always ensure you're using the perpendicular height, not the slant height, for calculating the area.

Determine (a) the area and (b) the perimeter of the quadrilateral. The figure shows a parallelogram with a base of 19 inches, a height of 4 inches, and a slant height (side) of 9 inches.

Learn how to find the area and perimeter of a parallelogram with a base of 19 inches, height of 4 inches, and slant height of 9 inches. Includes key geometric concepts and formulas. Suitable for students in Grades 6-8.

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