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find the polynomial that represents the area of a rhombus whose diagonals are ( 2P -4) and( 2P +4)​

Sagot :

xero099

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].

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