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### High School Mathematics - 29.20 Area of Quadrilateral

 The area of quadrilateral can be found by splitting it into two triangles and ading up their areas. The area of the quadrilateral whose vertices taken in order are A(x1, y1), B(x2, y2), C(x3, y3), D(x4, y4). Write down the coordinates as shown Area of Quad ABCD = Area of triangle ABC + Area of triangle ACD = 1/2{(x1y2)-(x2y1+(x2y3-x3y2(x3y1-x1y3)} + 1/2{(x1y3-x3y1)+x3y4-x4y3)+ (x4y1-x1y4} =1/2[(x1y2-x2y1)+(x2y3-x3y2)+(x3y4-x4y3)+(x4y1-x1y4)] Example: Find the area of the quadrilateral whose vertices are (3.4), (0,5),(2,-1) and (3,-2). The required area is 1/2[3x5-0x4+0x(-1)-5x2+2x(-2)-(-1)(3)+3x4-(-2)(3)] Answer: 11 sq.units Directions: Solve the following.
 Q 1: Find the area of the quadrilateral whose vertices are (1,1), (3,4), (5,-2) and (4,-7).41/235/239/2 Q 2: Find the area of the pentagon whose vertices are (-5,-2), (-2,5)(2,7), (5,1)and (2,-4).656664 Q 3: If the area of the quadrilateral whose angular points taken in order are (1,2), (-5,6), (7,4) and (h,-2), find h.356 Q 4: Find the area of the quadrilateral whose vertices are (1,1), (7,-3), (12,2) and (7,21).122132112 Q 5: Find the area of the pentagon whose vertices are (4,3), (-5,6),(0,-7), (3,-6), (-7,-2).979594 Q 6: The coordiantes of A, B, C, D are (6,3), (-3,5), (4,-2) and (x,3x) respectively. If triangle DBC/triangle ABC = 1/2, find x.11/85/25/4 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!