**Example 1:**

Find the lateral surface area of a box in the shape of prism whose bases are rectangular with side length $10$ cm and $12$ cm, and whose height is $5$ cm.

**Solution:**

**Given:**

Dimensions of rectangular prism are,

Length $(l)$ = $10$ cm

Breadth $(b)$ = $12$ cm

Height $(h)$ = $5$ cm

**Step 1:**

Perimeter of the rectangular prism is,

$P$ = $2(l + b)$

$\Rightarrow\ P$ = $2(10 + 12)$

= $2(22)$

= $44$

$\Rightarrow\ P$ = $44$ cm

**Step 2:**

Lateral Surface Area of Rectangular Prism = $Ph$ = $2h(l + b)$

$\Rightarrow\ LSA$ = $44 \times\ 5$

= $220$

Hence the lateral surface area of a box is $220\ cm^{2}$.

**Example 2:**

Find the volume of a rectangular solid with length $9$, width $6$, and height $5$.

**Solution:**

**Given:**

Dimensions of rectangular prism are,

Length $(l)$ = $9$

Width $(w)$ = $6$

Height $(h)$ = $5$

**Step 1:**

Area of the base of the prism,

Therefore, Area of the base = $l \times\ w$

$\Rightarrow\ A$ = $9 \times 6$

= $54$

$\Rightarrow\ A$ = $54$ square units

Step 2:

Volume of a rectangular prism = $Ah$

$\Rightarrow\ V$ = $54 \times 5$

= $270$

Hence the volume of the rectangular prism is $270$ square units.