The length, breadth and height of a cuboid are 15m, 6m and 5dm respectively. The lateral surface area of the cuboid is

Options

A. `45 m^(2)`
B. `21 m^(2)`
C. `201 m^(2)`
D. `90 m^(2)`

Explanation

To find the lateral surface area of a cuboid, we can use the formula:

**Lateral Surface Area (LSA) = 2 * (Length + Breadth) * Height**

### Step-by-step Solution:

1. **Identify the dimensions of the cuboid:**
- Length (L) = 15 m
- Breadth (B) = 6 m
- Height (H) = 5 dm

2. **Convert the height from decimeters to meters:**
- Since 1 dm = 0.1 m, we convert 5 dm to meters:
\[ H = 5 \, \text{dm} = 5 \times 0.1 \, \text{m} = 0.5 \, \text{m} \]

3. **Substitute the values into the Lateral Surface Area formula:**
\[ LSA = 2 \times (L + B) \times H \]
\[ LSA = 2 \times (15 \, \text{m} + 6 \, \text{m}) \times 0.5 \, \text{m} \]

4. **Calculate the sum of Length and Breadth:**
\[ L + B = 15 \, \text{m} + 6 \, \text{m} = 21 \, \text{m} \]

5. **Substitute this back into the LSA equation:**
\[ LSA = 2 \times 21 \, \text{m} \times 0.5 \, \text{m} \]

6. **Perform the multiplication:**
\[ LSA = 2 \times 21 \times 0.5 = 21 \, \text{m}^2 \]

### Final Answer:
The lateral surface area of the cuboid is **21 m²**.