# SAT Math Multiple Choice Question 672: Answer and Explanation

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**Question: 672**

**12.**

Note: Figure not drawn to scale.

In the figure above, if *m* || *l*, what is the area, in square units, of the shaded rectangle?

- A. 156
- B. 168
- C. 180
- D. 192

**Correct Answer:** D

**Explanation:**

**D**

**Special Topics (coordinate geometry) MEDIUM**

First, find the slope of *l* using the points (0, -9) and (12, 0):

Since the two lines are parallel, line *m* must also have a slope of . Now we can solve for *k* using the slope equation and the two points on line *m*, (0, 0) and (*k*, 12):

Cross multiply:

4(12) = 3(*k*)

Simplify:

48 = 3*k*

Divide by 3:

16 = *k*

Notice that the coordinates of the point (16, 12) correspond to the *width* and the *length* of the rectangle, respectively. Therefore, the area of the rectangle is 16 × 12 = 192 square units.