Final answer:
To find the area of a trapezoid with given vertex coordinates, the Shoelace formula can be used. This involves multiplying, summing, and subtracting specific products of the coordinates, then dividing by two after taking the absolute value.
Step-by-step explanation:
To calculate the area of a trapezoid with vertices A(-2,2), B(2,5), C(11,-7), and D(1,-2), you need to divide it into triangles and/or rectangles and find their areas before summing them up. Alternatively, you can use the Shoelace formula which is a mathematical algorithm to find the area of a polygon given the coordinates of its vertices.
To use the Shoelace formula, list the coordinates in a column, repeating the first point at the bottom. Multiply the x-coordinate of each point by the y-coordinate of the next point, summing those products. Then multiply the y-coordinate of each point by the x-coordinate of the next point, and sum those products. Subtract the second sum from the first, take the absolute value, and divide by 2 to get the area.
For our trapezoid:
- Compute the products of the coordinates in the order mentioned.
- Sum those products accordingly.
- Subtract, take the absolute value and divide by 2.
If done correctly, this process will yield the trapezoid's area.