Question

The area of a regular hexagon is 38cm^2. What is the area of a regular hexagon with sides four times as long?
A. 443.4in^2
B. 618.0in^2
C. 221.7in^2
D. 309.0in^2
Please help I am stuck on this question!

Answer 1

well what is 38*38

Answer 2

Area of a hexagon: \[A=\frac{3\sqrt{3}}{2}a^2\] but now \(a\implies 4a\) , so... \[A=\frac{3\sqrt{3}}{2}(4a)^2\]

Answer 3

So first find the legnth of the side.`

Answer 4

\[A=\frac{3\sqrt{3}}{2}a^2\]\[a=\sqrt{\frac{2A}{3\sqrt{3}}}\]once you find your side length, multiply it times 4 since it's 4 times as long.Finding that value, plug it back in to your equation and solve for your area.

Answer 5

If the measure of a linear dimension (such as a side) of a polygon changes by a scale factor of k, the area of the polygon changes by a scale factor of \(k^2\).