The perimeter of 4 squares is 24 cm, 32 cm, 40 cm, 48 cm respectively. What will be the area of the square having perimeter equal to sum of edges of 4 squares? (in sq.cm.)

Options

A. A)64
B. B)81
C. C)100
D. D)121

Answer

To solve the problem step by step, we will first calculate the sides of the squares from their perimeters, then find the perimeter of the new square, and finally calculate its area.

### Step 1: Calculate the sides of the squares from their perimeters.
The formula for the perimeter \( P \) of a square is given by:
\[ P = 4 \times \text{side} \]
Thus, the side of the square can be calculated as:
\[ \text{side} = \frac{P}{4} \]

- For the first square with perimeter \( 24 \, \text{cm} \):
\[ \text{side}_1 = \frac{24}{4} = 6 \, \text{cm} \]

- For the second square with perimeter \( 32 \, \text{cm} \):
\[ \text{side}_2 = \frac{32}{4} = 8 \, \text{cm} \]

- For the third square with perimeter \( 40 \, \text{cm} \):
\[ \text{side}_3 = \frac{40}{4} = 10 \, \text{cm} \]

- For the fourth square with perimeter \( 48 \, \text{cm} \):
\[ \text{side}_4 = \frac{48}{4} = 12 \, \text{cm} \]

### Step 2: Calculate the sum of the perimeters of the four squares.
Now, we need to find the total perimeter of these four squares:
\[ \text{Total Perimeter} = 24 + 32 + 40 + 48 \]
Calculating this gives:
\[ \text{Total Perimeter} = 144 \, \text{cm} \]

### Step 3: Find the perimeter of the new square.
The perimeter of the new square is equal to the total perimeter we just calculated:
\[ \text{Perimeter of new square} = 144 \, \text{cm} \]

### Step 4: Calculate the side of the new square.
Using the perimeter to find the side:
\[ \text{side}_{\text{new}} = \frac{144}{4} = 36 \, \text{cm} \]

### Step 5: Calculate the area of the new square.
The area \( A \) of a square is given by:
\[ A = \text{side} \times \text{side} \]
Thus, for our new square:
\[ A = 36 \times 36 = 1296 \, \text{cm}^2 \]

### Final Answer:
The area of the square having perimeter equal to the sum of the edges of the 4 squares is \( 1296 \, \text{cm}^2 \).

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