Question

The formula for the area of a parallelogram is A = bh, where b is the base and h is the height. A parallelogram that is not drawn to scale. The height is labeled (x minus 4) centimeters. The base is labeled (2 x squared + 2 x minus 6) centimeters. Which simplified expression represents the area of the parallelogram? –4x3 + 14x – 24 square centimeters 2x3 – 6x2 – 14x + 24 square centimeters –4x3 – 14x + 24 square centimeters 2x3 + 6x2 + 14x + 24 square centimeters

Answer 1

b

Explanation:

Answer 2

Option 2) 2x3 – 6x2 – 14x + 24 square centimeters

Explanation:

We know the Parallelogram Area is given by

`A=bh` Eqn. (1)

where

`b` : is the base

`h` : is the height

We are also given that the base is

`b=2x^2+2x-6`

and the height is

`h=x-4`

So we can plug these two expressions in Eqn. (1), simplify and find our Area equation as follow:

`A=(2x^2+2x-6)(x-4)\\\\A=(2x^2)(x)+(2x)(x)-(6)(x)+(2x^2)(-4)+(2x)(-4)-(6)(-4)\\\\A=2x^3+2x^2-6x-8x^2-8x+24\\\\A=2x^3+2x^2-8x^2-6x-8x+24\\\\A=2x^3-6x^2-14x+24`

Which matches Option 2. from the available ones.