Question

A rectangle has a height of x+4 and a width of x^2+3x+2.

Express the area of the entire rectangle.

Answer 1

Answer:

$area=x^3+7x^2+14x+8$

Step-by-step explanation:

the area of a rectangle is:

$area = height * width$

in this case we know the following:

height:$x+4$

width: $x^2+3x+2$

so to get the area we must muliply these two expressions:

$area=(x+4)(x^2+3x+2)$

and making the operations we get:

$area=(x+4)(x^2+3x+2)\\area=x^3+3x^2+2x+4x^2+12x+8$

adding the like terms:

$area=x^3+7x^2+14x+8$

the expression $x^3+7x^2+14x+8$ is the area of the entire rectangle

Answer 2

The area of a rectangle is the multiplication of its width and height.

The area of the rectangle is $x^3+7x^2+14x+8$.

Given:

The height of the rectangle is $x+4$.

The width of a rectangle is $x^2+3x+2$.

What is an area of a rectangle?

The area of a rectangle is a region that is bounded by four sides of the rectangle.

The formula of the area of a rectangle is as follows.

$\rm Area=width\times height$

Substitute the given value in the above equation.

${\rm Area}=(x+4)(x^2+3x+2)\\{\rm Area}=x^3+3x^2+2x+4x^2+12x+8$

Now add the like term.

${\rm Area}=x^3+7x^2+14x+8$

Thus, the area of the rectangle is $x^3+7x^2+14x+8$

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