The side of a rectangle is 6 more than its breadth. If the breadth is a, find the rule for finding the area of the rectangle. If the breadth of the rectangle is 8 cm, find its area.

Answer

To solve the problem step by step, we will first establish the relationship between the length and breadth of the rectangle, then derive the formula for the area, and finally calculate the area when the breadth is given as 8 cm.

### Step 1: Define the variables
Let the breadth of the rectangle be denoted as \( a \).

### Step 2: Express the length in terms of breadth
According to the problem, the length of the rectangle is 6 more than its breadth. Therefore, we can express the length \( l \) as:
\[ l = a + 6 \]

### Step 3: Write the formula for the area of the rectangle
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{breadth} \]
Substituting the expressions for length and breadth, we have:
\[ A = (a + 6) \times a \]

### Step 4: Expand the formula for area
Now, we will expand the expression:
\[ A = a \times a + 6 \times a \]
This simplifies to:
\[ A = a^2 + 6a \]
Thus, the rule for finding the area of the rectangle in terms of its breadth \( a \) is:
\[ A = a^2 + 6a \]

### Step 5: Calculate the area when the breadth is 8 cm
Now, we will find the area when the breadth \( a \) is 8 cm:
1. Substitute \( a = 8 \) into the area formula:
\[ A = 8^2 + 6 \times 8 \]
2. Calculate \( 8^2 \):
\[ 8^2 = 64 \]
3. Calculate \( 6 \times 8 \):
\[ 6 \times 8 = 48 \]
4. Add the two results together:
\[ A = 64 + 48 = 112 \]

### Final Answer
The area of the rectangle when the breadth is 8 cm is:
\[ A = 112 \, \text{cm}^2 \]

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