Given quadrilateral has vertices A (-5,2,5) B (-3,6,7) C (4,-1,5) D (2,-5,3)
Consider ΔABC
Area of ΔABC =
Here "X" represents a cross product.
⇒ 1/2 | (-3×-2)-(0×-7), (0×7) - (9×-2), (9×-7) - (-3×7)|
⇒ 1/2 |6, 18, -42|
⇒
⇒ 1062 sq units
Consider ΔACD
Area of ΔACD =
Here "X" represents cross product.
A (-5,2,5) C (4,-1,5) D (2,-5,3)
⇒ 1/2 | (-7×-2)-(-2×-4), (-2×-2) - (7×-2), (7×-4) - (-7×-2)|
⇒ 1/2 |6, 18, -42|
⇒
⇒ 1062 sq units
So, the area of the quadrilateral ABCD = Area of ΔABC + Area of ΔACD
= 1062 + 1062
= 2124 sq units