Answer. We use this information to find area of a quadrilateral when its vertices are given. If you get the area of a quadrilateral as a negative value, take it as positive. After having gone through the stuff given above, we hope that the students would have understood, how to find area of quadrilateral with vertices. That is, we always take the area of quadrilateral as positive. Now, Area of the quadrilateral ABCD = Area of triangle ABC + Area of triangle ACD If the points A(-3, 9) , B(a, b) and C(4, -5) are collinear and if a + b = 1 , then find a and b. Slope of line between (10,1). So, area of the quadrilateral ABCD is = (1/2) ⋅ {(x 1 y 2 + x 2 y 3 + x 3 y 4 + x 4 y 1)- (x 2 y 1 + x 3 y 2 + x 4 y 3 + x 1 y 4)} Problem : Find the area of the quadrilateral whose vertices are (-4, -2), (-3, -5), (3, -2) and (2, 3) Solution : Find the area of the each quadrilateral whose vertices are, (ii)  (-3, 4), (-5, -6), (4, -1) and (1, 2), (iii)  (-4, 5), (0, 7), (5, -5) and (-4, -2). Solution: quadrilateral whose vertices are (1,1), (2,4), (8,4) and (10,1). of the quadrilateral ABCD in order (counter clockwise direction) and write them column-wise as shown below. Tricks for finding the area of triangle and quadrilateral within 10 seconds. Let A(–4,–2), B(–3,–5), C (3,–2) and D(2,3) be the vertices of the quadrilateral ABC D. Area of a quadrilateral ABC D = Area of ABC + Area of AC D. By using a formula for the area of a triangle = 21. . Tips to learn Formula to find area of triangle. Then move a vertex so that one side becomes aligned with the first diagonal. By taking the points in counter clock wise, we have to find the area of CABD. By taking the points in counter clock wise direction, we find the area of BADC. Add the diagonal products x1y2, x2y3, x3y4 and x4y1 are shown in the dark arrows. Given : quadrilateral vertices are (1,1), (2,4), (8,4) and (10,1). units A r e a ( A B C D) = A r e a ( Δ A B C) + A r e a ( Δ A D C) = 8 + 11 = 19 s q. u n i t s. Example 1: A farmer has a pentagonal field ABCDE, which he divides into three triangular plots, as shown below: Arrange the plots in the order of increasing areas. The area is that of a triangle, half the cross-product of the diagonal vectors. The following pictorial representation helps us to write the above formula very easily. (-4, -2), B(-3, -5), C(3, -2) and (2, 3). =  (1/2)[(0 + 27 + 12 - 6) - (-54 + 0 + 3 + 16)], Find the value of k, if the area of a quadrilateral is 28 sq.units, whose vertices are (–4, –2), (–3, k), (3, –2) and (2, 3), Area of quadrilateral  =  28 square units, [(-4k  + 6 + 9 - 4) - (6 + 3k - 4 - 12)]  =  28(2). Click hereto get an answer to your question ️ Find the area of the quadrilateral ABCD whose vertices are A(1, 1) , B(7, 3) , C(12, 2) and D(7, 21) The area is then given by the formula Where x n is the x coordinate of vertex n, y n is the y coordinate of the nth vertex etc. Calculate the perimeter and area of the quadrilateral formed by the points (0,0) and (5,10) and (10,15) and (5,5) Multiply one side by itself to find the area of a square. Area(ABCD) =Area (ΔABC)+Area (ΔADC) =8 +11 = 19 sq. Thinking Corner : How many triangles exist, whose area is zero? Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here. if you need any other stuff in math, please use our google custom search here. So, area of the given quadrilateral is 28 square units. Let A(-4, -2), B(-3, -5), C(3, -2) and (2, 3). Because, the area of the quadrilateral is never negative. By applying the value of a in (2), we get. This transformation also preserves the area. Add the diagonal products x2y1, x3y2, x4y3 and x1y4 are shown in the dotted arrows. Find Area of Quadrilateral with Vertices : In this section, we will learn, how to how to find area of a quadrilateral with vertices. =  (1/2) x  {[20 + 6 + 9 - 4] - [6 - 15 - 4 - 12]}. Other Coordinate Geometry topics. Area of a triangle (By formula, given coordinates of vertices) Area of a triangle (Box method, given coordinates of vertices) Limitations The calculator will produce the wrong answer for crossed polygons, where one side crosses over another, as shown below. Squares are basically special rectangles, so … Subtract (2) from (1) and multiply the difference by 1/2 to get area of the quadrilateral ABCD. 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