Find the area of the trapezoid whose vertices are (4, 4), (10, 1), (1, 1), and (1, 4). (Your answer will be numerical only).

To find the area of a trapezoid with vertices at given coordinates, we can use the formula for the area of a trapezoid: A = 1/2 * (b1 + b2) * h, where b1 and b2 are the lengths of the bases (the parallel sides) and h is the height (the perpendicular distance between the bases).

First, we need to determine which sides of the trapezoid are the bases. In this case, the bases are the lines connecting the points (4, 4) and (1, 4), and the points (10, 1) and (1, 1).

The length of the first base (b1) can be found using the distance formula: sqrt((x2 - x1)^2 + (y2 - y1)^2). For the points (4, 4) and (1, 4), this gives us sqrt((4 - 1)^2 + (4 - 4)^2) = 3.

The length of the second base (b2) can be found in the same way. For the points (10, 1) and (1, 1), this gives us sqrt((10 - 1)^2 + (1 - 1)^2) = 9.

The height (h) of the trapezoid is the distance between the two bases. This is the y-coordinate of the points on the first base minus the y-coordinate of the points on the second base, or 4 - 1 = 3.

Substituting these values into the formula for the area of a trapezoid gives us A = 1/2 * (3 + 9) * 3 = 18. So, the area of the trapezoid is 18 square units.