Answer:
The scale factor used to go from P to Q is 1/4
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
If two figures are similar, then the ratio of its areas i equal to the scale factor squared
Let
z ----> the scale factor
x -----> area of polygon Q
y -----> area of polygon P
![z^{2}=\frac{x}{y}](https://tex.z-dn.net/?f=z%5E%7B2%7D%3D%5Cfrac%7Bx%7D%7By%7D)
we have
![y=72\ units^2](https://tex.z-dn.net/?f=y%3D72%5C%20units%5E2)
<em>Find the area of polygon Q</em>
Divide the the area of polygon Q in two triangles and three squares
The area of the polygon Q is equal to the area of two triangles plus the area of three squares
see the attached figure N 2
<em>Find the area of triangle 1</em>
![A=(1/2)(1)(2)=1\ units^2](https://tex.z-dn.net/?f=A%3D%281%2F2%29%281%29%282%29%3D1%5C%20units%5E2)
Find the area of three squares (A2,A3 and A4)
![A=3(1)^2=3\ units^2](https://tex.z-dn.net/?f=A%3D3%281%29%5E2%3D3%5C%20units%5E2)
<em>Find the area of triangle 5</em>
![A=(1/2)(1)(1)=0.5\ units^2](https://tex.z-dn.net/?f=A%3D%281%2F2%29%281%29%281%29%3D0.5%5C%20units%5E2)
The area of polygon Q is
![x=1+3+0.5=4.5\ units^2](https://tex.z-dn.net/?f=x%3D1%2B3%2B0.5%3D4.5%5C%20units%5E2)
Find the scale factor
![z^{2}=\frac{x}{y}](https://tex.z-dn.net/?f=z%5E%7B2%7D%3D%5Cfrac%7Bx%7D%7By%7D)
we have
![y=72\ units^2](https://tex.z-dn.net/?f=y%3D72%5C%20units%5E2)
![x=4.5\ units^2](https://tex.z-dn.net/?f=x%3D4.5%5C%20units%5E2)
substitute and solve for z
![z^{2}=\frac{4.5}{72}](https://tex.z-dn.net/?f=z%5E%7B2%7D%3D%5Cfrac%7B4.5%7D%7B72%7D)
![z^{2}=\frac{1}{16}](https://tex.z-dn.net/?f=z%5E%7B2%7D%3D%5Cfrac%7B1%7D%7B16%7D)
square root both sides
![z=\frac{1}{4}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B1%7D%7B4%7D)
therefore
The scale factor used to go from P to Q is 1/4