The area of a hexagon is 42 square cm. If all the dimesions of the hexagon are multiplied by 3, what will be the area of the new figure?
a) 126 cm2 b) 252 cm2, c) 378 cm 2 d) 14 cm2
I took 42 cm x 3 and got 126 cm2 did I work this correctly?
nope. If the side is x3, the area is x3^2 = x9 or 378
whenever the sides are scaled by a factor of n,
area is scaled by n^2
volume is scaled by n^3
since area is figured by multiplying two dimensions, each scaled by the same factor.
Yes, you worked it correctly. When the dimensions of a shape are multiplied by a certain factor, the area is also multiplied by the square of that factor.
In this case, the area of the original hexagon is 42 square cm. If all the dimensions of the hexagon are multiplied by 3, the new area will be 42 cm² x (3²) = 42 cm² x 9 = 378 cm².
Therefore, the correct answer is c) 378 cm².
To find the area of a hexagon, you need to use the formula:
Area = (3√3/2) * side^2
Given that the area of the original hexagon is 42 square cm, we can rearrange the formula to solve for the side length:
42 = (3√3/2) * side^2
Divide both sides by (3√3/2):
42 / (3√3/2) = side^2
To simplify, multiply both the numerator and denominator by 2:
(42 * 2) / (3√3) = side^2
Simplifying further:
84 / (3√3) = side^2
Now take the square root of both sides to find the side length:
√(84 / (3√3)) = side
Now we can find the area of the new hexagon by multiplying the side length by 3 and then using the formula:
Area of new hexagon = (3 * side)^2 = 9 * (side^2)
Substituting the value of the side length:
Area of new hexagon = 9 * (√(84 / (3√3))^2)
Simplifying:
Area of new hexagon = 9 * (84 / (3√3))
Dividing 84 by 3:
Area of new hexagon = 9 * (28 / √3)
To simplify further, multiply the numerator and denominator by √3:
Area of new hexagon = (9 * 28√3) / 3
Now, divide 9 by 3:
Area of new hexagon = 3 * 28√3
Calculating the value of 28√3 (approximately 48.498) and multiplying by 3, we get:
Area of new hexagon ≈ 3 * 48.498 ≈ 145.494
Therefore, the area of the new hexagon after multiplying the dimensions by 3 is approximately 145.494 square cm. None of the provided options match this answer, so I apologize for the discrepancy.