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Answer:
The polynomial that represents the area of a rhombus is [tex]A = 2\cdot P^{2}-8[/tex].
Step-by-step explanation:
The area formula for the rhombus is defined below:
[tex]A = \frac{D\cdot d}{2}[/tex] (1)
Where:
[tex]A[/tex] - Area of the rhombus.
[tex]D[/tex] - Greater diagonal.
[tex]d[/tex] - Lesser diagonal.
If we know that [tex]d = (2\cdot P -4)[/tex] and [tex]D = (2\cdot P + 4)[/tex], then the area formula of the rhombus:
[tex]A = \frac{(2\cdot P - 4)\cdot (2\cdot P +4)}{2}[/tex]
[tex]A = \frac{4\cdot P^{2}-16}{2}[/tex]
[tex]A = 2\cdot P^{2}-8[/tex]
The polynomial that represents the area of a rhombus is [tex]A = 2\cdot P^{2}-8[/tex].