What is the formula for the area of quadrilateral in coordinate geometry?įAQs on Area of a Triangle in Coordinate Geometry How Do You Find the Length of Side of a Triangle Using Coordinates?.If the distance between the points (2, 3) and (1, q) is 5, find the values of q.To find the area of a triangle in coordinate geometry, we need to find the length of three sides of a triangle using the distance formula.In case we get the answer in negative terms, we should consider the numerical value of the area, without the negative sign. The area of a triangle cannot be negative.Take the common term 1/2 outside the bracket. However, we should try to simplify it so that it is easy to remember.įor that, we simplify the product of the two brackets in each terms: The expression for the area of the triangle in terms of the coordinates of its vertices can thus be given as, Similarly, the bases and heights of the other two trapeziums can be easily calculated. BD and AE can easily be seen to be the y coordinates of B and A, while DE is the difference between the x coordinates of A and B. Its bases are BD and AE, and its height is DE. Trapezium Area = (1/2) × Sum of bases × HeightĬonsider any one trapezium, say BAED.
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Now, the area of a trapezium in terms of the lengths of the parallel sides (the bases of the trapezium) and the distance between the parallel sides (the height of the trapezium): We can express the area of a triangle in terms of the areas of these three trapeziums.Īrea(ΔABC) = Area(Trap.BAED) + Area(Trap.ACFE) - Area(Trap.BCFD) Notice that three trapeziums are formed: BAED, ACFE, and BCFD. In this figure, we have drawn perpendiculars AE, CF, and BD from the vertices of the triangle to the horizontal axis. In coordinate geometry, if we need to find the area of a triangle, we use the coordinates of the three vertices. How Do You Calculate the Area of A Triangle in Coordinate Geometry?