If the side of a square is reduced by 50%. Its area will be reduced by.
यदि वर्ग की भुजा को 50% तक कम कर दिया जाए तो उसका क्षेत्रफल कितना कम हो जाएगा?

Options

A. ` 75%`
B. ` 80%`
C. `60%`
D. `50%`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Define the original side of the square
Let the original side of the square be \( s \).

### Step 2: Calculate the area of the original square
The area \( A \) of a square is given by the formula:
\[ A = s^2 \]
So, the area of the original square is:
\[ A = s^2 \]

### Step 3: Calculate the new side after reducing by 50%
If the side is reduced by 50%, the new side \( s' \) will be:
\[ s' = s - 0.5s = 0.5s \]

### Step 4: Calculate the area of the new square
Now, we calculate the area of the new square with the reduced side:
\[ A' = (s')^2 = (0.5s)^2 = 0.25s^2 \]

### Step 5: Calculate the reduction in area
To find the reduction in area, we subtract the new area from the original area:
\[ \text{Reduction in area} = A - A' = s^2 - 0.25s^2 = 0.75s^2 \]

### Step 6: Calculate the percentage reduction in area
To find the percentage reduction in area, we use the formula:
\[ \text{Percentage reduction} = \left(\frac{\text{Reduction in area}}{\text{Original area}}\right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage reduction} = \left(\frac{0.75s^2}{s^2}\right) \times 100 = 75\% \]

### Conclusion
Thus, if the side of a square is reduced by 50%, its area will be reduced by **75%**.

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