Find the area of the quadrilateral ABCD, the coordinates of whose vertices are A(6,-3), B(-4,-2), C(3,1) and D(5,0)?
- ((a))
21 unit2
- ((b))
30 unit2
- ((c))
25 unit2
- ((d))
18 unit2
Show Answer
21 unit2
Given:
The coordinates of the vertices of quadrilateral ABCD are A(6, -3), B(-4, -2), C(3, 1), and D(5, 0).
Formula Used:
The area of a quadrilateral given its vertices (x1, y1), (x2, y2), (x3, y3), and (x4, y4) is:
Area = (1/2) | x1y2 + x2y3 + x3y4 + x4y1 - (y1x2 + y2x3 + y3x4 + y4x1) |
Calculation:
Substituting the given coordinates:
Area = (1/2) | 6(-2) + (-4)1 + 3(0) + 5(-3) - (-3(-4) + (-2)3 + 1(5) + 0(6)) |
⇒ Area = (1/2) | -12 - 4 + 0 - 15 - (12 - 6 + 5 + 0) |
⇒ Area = (1/2) | -31 - 11 |
⇒ Area = (1/2) | -42 |
⇒ Area = (1/2) × 42
⇒ Area = 21
∴ The correct answer is 21 unit2.




















































