Chapter 4.3, Problem 40WE

To determine

To calculate: The total surface area of the solid.

Answer to Problem 40WE

The total surface area of the solid is $54a^2$ .

Explanation of Solution

Given information:

The solid is provided below,

Formula used:

The total surface area is sum of area of all faces of a solid.

The area of rectangle with length l , width bis $A=lb$ .

The area of square with side sis $A=s^2$ .

Calculation:

Consider thesolid provided below,

Recall that the total surface area is sum of area of all faces of a solid.

Compute the areas of all the faces in the figure provided above.

The back side of the figure is a rectangle with length $4a$ and width $3a$ .

Therefore, area is

  $\begin{array}{c}{A}_1=\left(4a\right)\left(3a\right)\\ =12a^2\end{array}$

For the front side

There are 4 rectangles with length $a$ and width $3a$ .

Therefore, area is

  $\begin{array}{c}{A}_2=4\left(a\right)\left(3a\right)\\ =12a^2\end{array}$

Also, there are two big rectangles on each side with length $2a$ and width $3a$ .

Therefore, area is

  $\begin{array}{c}{A}_3=2\left(2a\right)\left(3a\right)\\ =12a^2\end{array}$

And, there are 3 rectangles on top and 3 on bottom with length $a$ and width $2a$ .

Therefore, area is

  $\begin{array}{c}{A}_4=9\left(a\right)\left(2a\right)\\ =18a^2\end{array}$

Total surface area is, apply it,

  $\begin{array}{c}\text{TSA}=A_1+A_2+A_3+A_4\\ =12a^2+12a^2+12a^2+18a^2\\ =54a^2\end{array}$

Thus, the total surface area of the solid is $54a^2$ .