Question

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

Answer 1

The polynomial that represents the area of a rhombus is
`A = 2\cdot P^(2)-8`.

Explanation:

The area formula for the rhombus is defined below:

`A = (D\cdot d)/(2)` (1)

Where:

`A` - Area of the rhombus.

`D` - Greater diagonal.

`d` - Lesser diagonal.

If we know that
`d = (2\cdot P -4)` and
`D = (2\cdot P + 4)`, then the area formula of the rhombus:

`A = ((2\cdot P - 4)\cdot (2\cdot P +4))/(2)`

`A = (4\cdot P^(2)-16)/(2)`

`A = 2\cdot P^(2)-8`

The polynomial that represents the area of a rhombus is
`A = 2\cdot P^(2)-8`.