If l,b,h be the length, breadth and height of a cuhoid, then its lateral surface area =(………………)sq units.

Answer

To find the lateral surface area (LSA) of a cuboid with length \( L \), breadth \( B \), and height \( H \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition**: The lateral surface area of a cuboid is the area of the vertical sides, excluding the top and bottom surfaces.

**Hint**: Remember that lateral surface area only considers the sides that are vertical.

2. **Identify the Vertical Faces**: A cuboid has four vertical faces. The pairs of opposite faces are:
- Two faces with dimensions \( L \) (length) and \( H \) (height).
- Two faces with dimensions \( B \) (breadth) and \( H \) (height).

**Hint**: Visualize the cuboid and identify the vertical sides.

3. **Calculate the Area of Each Pair of Faces**:
- The area of one face with dimensions \( L \) and \( H \) is \( L \times H \). Since there are two such faces, their total area is \( 2 \times (L \times H) = 2LH \).
- The area of one face with dimensions \( B \) and \( H \) is \( B \times H \). Similarly, for two such faces, the total area is \( 2 \times (B \times H) = 2BH \).

**Hint**: Use the formula for the area of a rectangle (length × breadth) to find the area of each face.

4. **Combine the Areas**: Now, add the areas of the two pairs of vertical faces:
\[ \text{Lateral Surface Area (LSA)} = 2LH + 2BH \]

**Hint**: Make sure to combine like terms correctly.

5. **Factor Out Common Terms**: We can factor out the common terms from the expression:
\[ \text{LSA} = 2H(L + B) \]

**Hint**: Look for common factors in the expression to simplify it.

### Final Answer:
The lateral surface area of the cuboid is given by:
\[ \text{Lateral Surface Area} = 2H(L + B) \text{ square units} \]