111. The sum of the length, breadth and height of a cuboid is 38 cm and the length of its $$ \vee \backslash $$ diagonal is 22 cm . Find the surface area of the cuboid. Given : $$ 1+b+h=38 $$ and $$ P^{2}+b^{2}+h^{2}=22^{2} $$ To find : $$ 2(l b+b h+h l) $$

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To determine the surface area of the cuboid, we'll follow these steps:

### Given:
1. **Sum of dimensions:**
   $$
   l + b + h = 38 \quad \text{(1)}
   $$
2. **Space diagonal:**
   $$
   \sqrt{l^2 + b^2 + h^2} = 22 \ \Rightarrow \ l^2 + b^2 + h^2 = 22^2 = 484 \quad \text{(2)}
   $$

### To Find:
$$
\text{Surface Area} = 2(lb + bh + hl)
$$

### Step-by-Step Solution:

1. **Square the Sum of Dimensions:**
   $$
   (l + b + h)^2 = l^2 + b^2 + h^2 + 2(lb + bh + hl)
   $$
   Plugging in the known values:
   $$
   38^2 = 484 + 2(lb + bh + hl)
   $$
   $$
   1444 = 484 + 2(lb + bh + hl)
   $$

2. **Solve for $$ lb + bh + hl $$:**
   $$
   1444 - 484 = 2(lb + bh + hl)
   $$
   $$
   960 = 2(lb + bh + hl)
   $$
   $$
   lb + bh + hl = \frac{960}{2} = 480
   $$

3. **Calculate the Surface Area:**
   $$
   \text{Surface Area} = 2(lb + bh + hl) = 2 \times 480 = 960 \ \text{cm}^2
   $$

### **Answer:**  
The surface area of the cuboid is **960 cm²**.
The surface area of the cuboid is 960 cm².

The sum of the length, breadth and height of
a cuboid is 38 cm and the length of its
diagonal is 22 cm . Find the surface area of
the cuboid.
Given : and
To find :

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The sum of the length, breadth and height of a cuboid is 38 cm and the length of its diagonal is 22 cm . Find the surface area of the cuboid. Given : and To find :