Chapter 4.5, Problem 41WE

To determine

To find: the area of the given shaded region

Answer to Problem 41WE

The area of the given shaded region is : $\boxed{3x^2+31x}$

Explanation of Solution

Given information: The shaded region is given below

  

Concept Involved:

Identify the area of larger rectangle. Identify the area of smaller rectangle. If we find the difference between the area of larger and smaller rectangle, then that would be the area of shaded region.

Formula Used:

Area of rectangle = $Length\times Width$

Calculation:

Identify the area of larger rectangle.

Length of larger rectangle = $x+9$

Width of larger rectangle = $3x$

Area of larger rectangle = $\left(x+9\right)\cdot \left(3x\right)$

Identify the area of smaller rectangle.

Length of smaller rectangle = $4$

Width of smaller rectangle = $x$

Area of smaller rectangle = $4\cdot x$

Area of the shaded region is found by subtracting the area of smaller rectangle from area of larger rectangle

  $\left(x+9\right)\cdot \left(3x\right)+4\cdot x$

Distribute the 3x in the expression $\left(x+9\right)\cdot \left(3x\right)+4\cdot x$

  $3x^2+27x+4x$

Combine like terms

  $3x^2+31x$

Conclusion:

The area of the shaded region given is $\boxed{3x^2+31x}$