To solve the problem, let’s calculate:

Part (a): Area of the quadrilateral

The shape appears to be a parallelogram, so the formula for the area is:

$\text{Area} = \text{Base} \times \text{Height}$

Here:

• Base ($b$) = 17 in.
• Height ($h$) = 4 in.

$\text{Area} = 17 \times 4 = 68 \, \text{square inches.}$

Part (b): Perimeter of the quadrilateral

The formula for the perimeter of a parallelogram is:

$\text{Perimeter} = 2 \times (\text{Base} + \text{Side Length})$

Here:

• Base ($b$) = 17 in.
• Side length ($s$) = 9 in.

$\text{Perimeter} = 2 \times (17 + 9) = 2 \times 26 = 52 \, \text{inches.}$

Final Results:

• Area: $68 \, \text{in}^2$
• Perimeter: $52 \, \text{in.}$

Would you like a detailed explanation of any of the steps?

Related Questions:

1. How is the area of a parallelogram different from other quadrilaterals?
2. Can the height of a parallelogram be located outside the shape?
3. What is the formula for the area of other quadrilaterals like trapezoids or rectangles?
4. How does changing the height affect the area of a parallelogram?
5. Why is the perimeter calculated using twice the sum of the base and side?

Tip:

Always ensure the height is measured perpendicular to the base for accurate area calculations.