To calculate the area of the given quadrilateral:

Step 1: Break the quadrilateral into simple shapes

The quadrilateral can be divided into two parts:

1. A rectangle on the left with dimensions $10 \times 10$.
2. A right triangle on the right with a base of 10 and a height of 16.

Step 2: Calculate the area of each shape

1. Rectangle area: $\text{Area of rectangle} = \text{length} \times \text{width} = 10 \times 10 = 100$

2. Triangle area: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 16 = 80$

Step 3: Add the areas

$\text{Total area of the quadrilateral} = \text{Area of rectangle} + \text{Area of triangle} = 100 + 80 = 180$

It appears the given answer choices may not match this calculation. Please confirm the dimensions or context for accuracy.

Do you have any questions or would you like more detailed steps? Here are some related questions for further exploration:

1. How can different methods of dividing a quadrilateral affect area calculations?
2. Why is the area of a triangle calculated using $\frac{1}{2} \times \text{base} \times \text{height}$?
3. What happens if one of the dimensions is adjusted? How would that affect the area?
4. Could this shape be represented with other simple geometric shapes for area calculation?
5. What real-life problems require breaking complex shapes into simpler ones?

Tip: Always verify the base and height of triangles carefully; they must be perpendicular to each other!