First, let's find the area of one face of the original cube. Since all sides are 2 cm, the area of one face is 2 cm x 2 cm = 4 cm^2.
Now, when the cube is enlarged with a scale factor of 3, all sides will become 2 cm x 3 = 6 cm. And since a hexagon is made up of 6 equilateral triangles, we need to find the area of one equilateral triangle.
Each side of the equilateral triangle will be the same length as the side of the enlarged cube, so the side length of the triangle is 6 cm. The formula for the area of an equilateral triangle is A = (s^2 * √3) / 4, where s is the side length.
Substitute s = 6 cm into the formula:
A = (6^2 * √3) / 4
A = (36 * 1.732) / 4
A = 62.352 / 4
A = 15.588 cm^2
Since there are 6 equilateral triangles that make up the hexagon, the total area of the hexagon will be 6 triangles x 15.588 cm^2 = 93.528 cm^2.
Therefore, the area of the hexagon when the cube is enlarged with a scale factor of 3 will be 93.528 cm^2.
A cube has all sides of length 2 cm . What will the area of the hexagon be,if it is enlarged with scale factor 3?
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