A cubical gift box has each side measuring 12.4 cm. It is to be wrapped all over with a gift paper. Find the area to be wrapped.

Correct Answer: The correct option is 922.56 cm².

Step-by-Step Explanation:

1. Understand the Problem:
A cubical gift box needs to be wrapped all over with gift paper. Wrapping it "all over" means covering all 6 faces of the cube. Therefore, the area of the gift paper required is equal to the total surface area (TSA) of the cubical box.

2. Formula for Total Surface Area of a Cube:
The total surface area of a cube with side length a is given by:

$\text{Total Surface Area}=6\times a^2$

3. Calculate the Area:
Given side length of the cube, a = 12.4 cm.

$\text{Area to be wrapped}=6\times {\left(12.4\right)}^2$

$\text{First, find}{\left(12.4\right)}^2:$

$12.4\times 12.4=153.76{\text{cm}}^2$

$\text{Now multiply by 6:}$

$\text{Total Surface Area}=6\times 153.76=922.56{\text{cm}}^2$

Thus, the area of gift paper needed to wrap the box completely is 922.56 cm².