Answer:
Step-by-step explanation:
The diagonal of the parallelogram ABCD divides it into 2 equal triangles. Considering triangle ABC, it means that the area of the parallelogram would be
2 × area of triangle ABC
Writing the vertices of triangle ABC,
A(−1,3,3), B(0,5,7), C(1,2,6)
We would determine the length of each side of the triangle.
AB = √(0 - - 1)² + (5 - 3)² + (7 - 3)^2
AB = √(1 + 4 + 16) = √21
BC = √(1 - 0)² + (2 - 5)² + (6 - 7)²
BC = √(1 + 9 + 1) = √11
AC = √(1 - - 1)² + (2 - 3)² + (6 - 3)²)
AC = √(4 + 1 + 9) = √14
We would apply the heron's formula for determining the area of a triangle
Area = √s(s - a)(s - b)(s - c)
Where
s = (a + b + c)/2
a = AB, b = BC, c = AC
s = (√21 + √11 + √14)/2 = 5.82
s - a = 5.82 - √21 = 1.24
s - b = 5.82 - √11 = 2.5
s - c = 5.82 - √14 = 2.08
Area = √(5.82 × 1.24 × 2.5 × 2.08) = 6.126
Therefore, area of parallelogram ABCD is
6.126 × 2 = 12.252
