Question

The area of a hexagon is 42 square centimeters. If all the dimensions of the hexagon are multiplied by 3, what will be the area of the new figure? 126 cm^ 252 cm^ 378 cm^ 14 cm^

Answer 1

C.
`378\text{ cm}^2`

Explanation:

We have been given that the area of a hexagon is 42 square centimeters. We are asked to find the area of the hexagon, when all the dimensions of the hexagon are multiplied by 3.

We will use area of hexagon formula to solve our given problem.

`\text{Area of hexagon}=(3√(3))/(2)* a^2`, where a is length of each side of hexagon.

Since in the area of hexagon formula we square the length of each side of hexagon, so the area of the new hexagon would be square of 3 times the area of original hexagon.

`\text{Area of new hexagon}=42\text{ cm}^2* 3^2`

`\text{Area of new hexagon}=42\text{ cm}^2* 9`

`\text{Area of new hexagon}=378\text{ cm}^2`

Therefore, the area of new figure would be 378 square centimeters and option C is the correct choice.

Answer 2

The area ratio is the square of the scale factor. The new area will be
3² × 42 cm² = 378 cm²