Chapter SH, Problem 12.5.5EP

To determine

To find: the lateral area and surface area of a rectangular prism.

Answer to Problem 12.5.5EP

The lateral area and surface area are respectively $224{\text{mm}}^2,351.68{\text{mm}}^2$ .

Explanation of Solution

Given:

Length is 7.6 mm.

Width is 8.4 mm.

Height is 7.0 mm.

Formula used:

Lateral area of the prism is $L=Ph$

Total surface area of the prism is $S=L+2B$

Calculation:

Lateral area of the prism is

  $L=Ph$

Here P is the base perimeter and h is the height.

Total surface area of the prism is

  $S=L+2B$

Here 2B is the area of two bases.

Perimeter of the base of a rectangular prism is

  $\begin{array}{c}P=2\left(\text{length}+\text{width}\right)\\ =2\left(7.6+8.4\right)\\ =32\end{array}$

Area of the base is $\text{length}\times \text{width}$ .

  $\begin{array}{c}B=\text{ length}\times \text{width}\\ =7.6\times 8.4\\ =63.84\end{array}$

Height is h = 7 mm.

Lateral area is

  $\begin{array}{c}L=Ph\\ =32\times 7\\ =224\end{array}$

Surface area is

  $\begin{array}{c}S=L+2B\\ =224+2\times 63.84\\ =351.68\end{array}$

Conclusion:

Hence, the lateral area and surface area are respectively $224{\text{mm}}^2,351.68{\text{mm}}^2$ .