Question

Determine the area of the shaded region in square units. A rectangular coordinate system has a horizontal axis with values from 0 to 7 and a vertical axis with values from 0 to 3.5.

A line segment starts at (0, 3), goes horizontally right, and ends at (6, 3).
The region below the line segment and above the horizontal axis is shaded between 1 and 3 on the horizontal axis.

Answer 1

The area of the shaded region is calculated using the formula for the area of a rectangle, which is base × height. The base is 2 units long (from 1 to 3 on the horizontal axis), and the height is 3 units. The area of the shaded rectangle is thus 6 square units.

Step-by-step explanation:

To find the area of the shaded region described, we imagine a rectangle under the line segment with its top side being the line segment. The line starts at (0, 3) and extends to (6, 3), being perfectly horizontal, and the shaded region is between the coordinates (1, 0) and (3, 3). The area of the shaded region can be calculated using the formula for the area of a rectangle, which is base × height.

The base of the shaded rectangle extends from 1 to 3 on the horizontal axis, which gives us a length of 2 units (base). The height is given by the y-coordinate of the line segment, which is 3 units, since the region is above the horizontal axis and below the line (height).

Now, calculating the area:

AREA = base × height
= 2 units × 3 units
= 6 square units.

Therefore, the area of the shaded region is 6 square units.