A rectangular plot of land measures `45mxx30m`. A boundary wall of height 2.4 m is built all around the plot at a distance of 1 m from the plot. Find the area of the inner surface of the boundary wall.

Answer

To find the area of the inner surface of the boundary wall around a rectangular plot of land measuring 45 m by 30 m, we will follow these steps:

### Step 1: Determine the dimensions of the boundary wall
The boundary wall is built at a distance of 1 meter from the plot. Therefore, we need to add 1 meter to each side of the plot's dimensions.

- Length of the plot = 45 m
- Breadth of the plot = 30 m

**Calculating the dimensions of the boundary wall:**
- Length of the boundary wall = Length of the plot + 1 m (on one side) + 1 m (on the other side)
= 45 m + 1 m + 1 m = 47 m

- Breadth of the boundary wall = Breadth of the plot + 1 m (on one side) + 1 m (on the other side)
= 30 m + 1 m + 1 m = 32 m

### Step 2: Determine the height of the boundary wall
The height of the boundary wall is given as 2.4 m.

### Step 3: Calculate the area of the inner surface of the boundary wall
The inner surface area of the boundary wall consists of four walls: two walls of length and two walls of breadth.

**Using the formula for the area of the walls:**
- Area of two longer walls = 2 × (Length of the boundary wall × Height of the wall)
= 2 × (47 m × 2.4 m)
= 2 × 112.8 m²
= 225.6 m²

- Area of two shorter walls = 2 × (Breadth of the boundary wall × Height of the wall)
= 2 × (32 m × 2.4 m)
= 2 × 76.8 m²
= 153.6 m²

**Total inner surface area of the boundary wall:**
Total area = Area of longer walls + Area of shorter walls
= 225.6 m² + 153.6 m²
= 379.2 m²

### Final Answer
The area of the inner surface of the boundary wall is **379.2 m²**.

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