The area of the parallelogram will be 108 square units.
<h3>What is the area of the parallelogram?</h3>
The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
The vertices of the parallelogram are (x₁, y₁), (x₂, y₂), (x₃, y₃), and ( x₄, y₄).
Then the area of the parallelogram will be calculated as below:-
Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₄+x₄y₁) - (y₁x₂ + y₂x₃ + y₃x₄+y₄x₁)]|
We have
(x₁, y₁) ⇒ (-12, 2)
(x₂, y₂) ⇒ (6, 2)
(x₃, y₃) ⇒ (-2, -3)
(x₄, y₄) ⇒ (-20 , -3 )
Then the area will be
Area = 1/2[{(-12) x (2) + (6) x (-3) + (-2) x (-3) + (-20 x 2 )} – {(2) x (6) + (2) x (-2) + (-3) x (-20) + ( -3 ) ( -12 )}]
Area = 108 / 2
Area = 54 square units.
Therefore, the area of the parallelogram will be 108 square units.
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