Question

hexagon b is a scaled copy of hexagon a.
what scale factor takes hexagon a to hexagon b?

Explanation:

Step1: Identify the corresponding sides

Hexagon A has a side length of \(4\frac{1}{2}=\frac{9}{2}\), and hexagon B has a corresponding side length of \(10\frac{1}{2}=\frac{21}{2}\).

Step2: Calculate the scale factor

The scale factor \(k\) is given by the formula \(k=\frac{\text{side length of B}}{\text{side length of A}}\).
So, \(k = \frac{\frac{21}{2}}{\frac{9}{2}}\).
Since dividing by a fraction is the same as multiplying by its reciprocal, \(k=\frac{21}{2}\times\frac{2}{9}\).
The \(2\)s cancel out, and \(k=\frac{21}{9}=\frac{7}{3}\).

Answer:

\(\frac{7}{3}\)