Chapter 11.4, Problem 25PPS

To determine

To find: The area of the shaded region.

Answer to Problem 25PPS

The area of the given figure is $50.9{\text{ft}}^2$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the area of the vertical rectangular part of the total floor plan is $A_1$ . Then, the area of the plan is,

  $\begin{array}{c}{A}_1=\left(2+\frac{11}{12}\right)\left(4+\frac{10}{12}\right)\\ =\frac{35}{12}\left(\frac{58}{12}\right)\\ =14.1{\text{ft}}^2\end{array}$

Consider the area of the horizontal part of the total floor plan is $A_2$ then,

  $\begin{array}{c}{A}_2=8^{\prime }\times 2^{\prime }\times 10^{″}\\ =\left(2+\frac{10}{12}\right)8\\ =\frac{34}{12}\left(8\right)\\ =22.7{\text{ft}}^2\end{array}$

Suppose that the area of the triangle of the total floor plan is $A_3$ . Then, the height of the triangle is,

  $\begin{array}{l}{h}^2=\left(5^{\prime }{4}^{″}\right)-4^2\\ h^2={\left(5+\frac{1}{3}\right)}^2-16\\ h^2=\frac{256}{9}-16\\ h=3.5\end{array}$

Then, the area of the triangle is,

  $\begin{array}{c}{A}_3=\frac{1}{2}\left(b\right)\left(h\right)\\ =\frac{1}{2}\left(8\right)\left(3.5\right)\\ =14.1\end{array}$

Thus, the total area of the floor plan is $14.1+22.7+14.1=50.9{\text{ft}}^2$ .

Thus, the area of the given figure is $50.9{\text{ft}}^2$ .