Answer:
To find the area of a trapezoid, we need to know the lengths of its parallel bases and its height. In this case, we are given the coordinates of the trapezoid’s vertices: A(0, 3), B(3, 2), C(3, -1), and D(0, -3).
First, let’s calculate the lengths of the bases. The bases of a trapezoid are the two parallel sides.
Base 1 (AB): The distance between points A and B can be found using the distance formula:
AB = √((x2 - x1)^2 + (y2 - y1)^2) = √((3 - 0)^2 + (2 - 3)^2) = √(9 + 1) = √10
Base 2 (CD): The distance between points C and D can be calculated in the same way:
CD = √((x2 - x1)^2 + (y2 - y1)^2) = √((3 - 0)^2 + (-1 - (-3))^2) = √(9 + 4) = √13
Next, let’s determine the height of the trapezoid. The height is the perpendicular distance between the bases.
To find the height, we need to find the length of the vertical segment that connects points A and D. Since points A and D have the same x-coordinate (0), the height is simply the difference in their y-coordinates:
Height (AD) = | y2 - y1 | = | 3 - (-3) | = 6
Finally, we can use the formula to calculate the area of the trapezoid:
Area = 0.5 * (base1 + base2) * height
= 0.5 * (√10 + √13) * 6
≈ 18.73 square units
So, the area of the trapezoid bounded by the given coordinates is approximately 18.73 square units.