Answer:
Area of the first region is 6 square meters.
Area of the second region is 12 square meters.
Area of the third region is 24 square meters.
Step-by-step explanation:
Given:
Total area of the region, [tex]A=42\textrm{ }m^{2}[/tex]
Let area of the first region be [tex]x[/tex].
As per question,
Area of second region is twice the first. So, area, [tex]A_{2}=2x[/tex]
Area of third region is twice the second. So, area, [tex]A_{3}=2A_{2}=2(2x)=4x[/tex]
Now, total area is the sum of the areas of the three regions. So,
[tex]x+A_{2}+A_{3}=A\\x+2x+4x=42\\7x=42\\x=\frac{42}{7}=6\textrm{ }m^{2}[/tex]
Therefore, area of first region is [tex]6\textrm{ }m^{2}[/tex]
Area of second region is, [tex]A_{2}=2x=2\times 6 = 12\textrm{ }m^{2}[/tex]
Area of third region is, [tex]A_{3}=4x=4\times 6 = 24\textrm{ }m^{2}[/tex]
