Chapter 7.2, Problem 33P

Find the area of each figure.

To determine

To calculate: The area of the figure

Answer to Problem 33P

The area of the rectangle is $4x^3\left(3x+2\right)$ square units.

Explanation of Solution

Given information:

The figure is provided below,

Formula used:

Area $\left(A\right)$ of rectangle is product of its length $\left(l\right)$ and breadth $\left(b\right)$ . It is mathematically denoted by $A=l\times b$ .

Calculation:

Consider the provided figure,

The above figure is a rectangle as its opposite sides are equal and each angle is right angle. So, length is $\left(3x^2+2x\right)$ and breadth is $4x^2$ .

Recall that area $\left(A\right)$ of rectangle is product of its length $\left(l\right)$ and breadth $\left(b\right)$ . It is mathematically denoted by $A=l\times b$ .

Apply it,

$\begin{array}{c}A=l\times b\\ =\left(3x^2+2x\right)\times \left(4x^2\right)\\ =3x^2\left(4x^2\right)+2x\left(4x^2\right)\\ =12x^4+8x^3\end{array}$

Simplify it further as,

$\begin{array}{c}A=12x^4+8x^3\\ =4x^3\left(3x+2\right)\end{array}$

Thus, the area of the figure is $4x^3\left(3x+2\right)$ square units.