What method can be used to calculate area through coordinates?

The method referred to as "Area by coordinates" is designed specifically to compute the area of simple polygons using the coordinates of their vertices. This technique utilizes the coordinates of the points that define the polygon and applies a formula that involves these coordinates to determine the area enclosed by the shape.

The formula typically used in this method is known as the shoelace formula or surveyor's formula, which calculates the area by summing the products of the coordinates in a specific manner. This method is particularly effective for polygons that may not have straight sides or regular shapes, providing a way to find the total area based on the vertices' coordinates.

In contrast, the other methods listed, like the Average End Area Method and the Trapezoidal Rule, serve different purposes primarily in calculus and civil engineering for volume calculation or numerical integration. The Distance Formula is used to find the length of line segments between two points rather than for area calculation. Hence, these alternatives would not apply directly to the question of calculating area through coordinates in the context specified.