Q:

How do you calculate the area of a triangle with its vertices?

A:

The area of a triangle can be calculated from its vertices by using a formula to find the distances between them. This allows for the calculation of the area of a parallelogram with the same base and height as the triangle. Then, this figure is divided by two.

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A triangle's vertices represent the points of the triangle on a grid, and are written as the x and y coordinates of each point. The points can be referred to as point A, point B and point C. The formula for calculating the area of such a triangle is as follows:

1. The y coordinate of point C must be subtracted from the y coordinate of point B. This number must be multiplied by the x coordinate of point A.
2.
3. The y coordinate of point A must be subtracted from the y coordinate of point C. This number must be multiplied by the x coordinate of point B.
4.
5. The y coordinate of point B must be subtracted from the y coordinate of point A. This number must be multiplied by the x coordinate of point C.
6. The products of the calculations performed in Steps 1 to 3 must be added. Finally, this number is divided by two. The resulting number is the area of the triangle.
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