The area of the parallelogram is approximately equal to 59.994 square units.
How to determine the area of a parallelogram by using Heron's formula
The area of a parallelogram is equivalent to the sum of the areas of the two triangles by adding a diagonal. Then, the area of each triangle can be found in terms of side terms by Heron's formula. First, find the length of each side:
Side AB
AB = (4, 6) - (- 2, 6)
AB = (6, 0)
AB = √(6² + 0²)
AB = 6
Side CD
CD = (- 1, - 4) - (5, - 4)
CD = (- 6, 0)
CD = √(6² + 0²)
CD = 6
Side AD
AD = (- 1, - 4) - (- 2, 6)
AD = (1, 10)
AD = √(1² + 10²)
AD = √101
Side BC
BC = (5, - 4) - (4, 6)
BC = (1, - 10)
BC = √[1² + (- 10)²]
BC = √101
Side AC
AC = (5, - 4) - (- 2, 6)
AC = (7, - 10)
AC = √[7² + (- 10)²]
AC = √149
Second, determine the areas of the two triangles.
Triangle ABC
s = 0.5 · (AB + BC + AC)
s ≈ 14.128
A = √[s · (s - AB) · (s - BC) · (s - AC)]
A ≈ 29.997
Triangle ACD
s = 0.5 · (AC + CD + AD)
s ≈ 14.128
A = √[s · (s - AC) · (s - CD) · (s - AD)]
A ≈ 29.997
Third, find the area of the parallelogram by adding the two areas calculated in the previous step:
A' = 29.997 + 29.997
A' = 59.994
The area of the parallelogram is approximately equal to 59.994 square units.
To learn more on Heron's formula: https://brainly.com/question/22391198
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