Each diagonal of a square is 14 cm long. Its area is

Options

A. `196 cm^(2)`
B. `88 cm^(2)`
C. `98 cm^(2)`
D. `147 cm^(2)`

Answer

To find the area of a square when each diagonal is given, we can follow these steps:

### Step 1: Understand the relationship between the diagonal and the side of the square.
In a square, the diagonal divides the square into two right-angled triangles. According to the Pythagorean theorem, the relationship between the side length (a) and the diagonal (d) is given by:
\[ d^2 = a^2 + a^2 \]
This simplifies to:
\[ d^2 = 2a^2 \]

### Step 2: Substitute the given diagonal length into the equation.
We know the diagonal (d) is 14 cm. Therefore, we can substitute this value into the equation:
\[ 14^2 = 2a^2 \]

### Step 3: Calculate \( 14^2 \).
Calculating \( 14^2 \):
\[ 14^2 = 196 \]
So, we have:
\[ 196 = 2a^2 \]

### Step 4: Solve for \( a^2 \).
Now, we can solve for \( a^2 \) by dividing both sides of the equation by 2:
\[ a^2 = \frac{196}{2} \]
\[ a^2 = 98 \]

### Step 5: Find the area of the square.
The area (A) of a square is given by the formula:
\[ A = a^2 \]
Since we found \( a^2 = 98 \), we can conclude:
\[ A = 98 \, \text{cm}^2 \]

### Final Answer:
The area of the square is \( 98 \, \text{cm}^2 \).

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