Answer:
[tex]Area =\frac{10x + 15}{2}[/tex] in both cases
Step-by-step explanation:
See attachment for complete question.
From the attachment, we have the following given parameters
Green Section: Dimension: x by 2
Orange Section: Dimension: 2 by [tex]1\frac{1}{2}[/tex]
Purple Section: Dimension: 3 by (x + [tex]1\frac{1}{2}[/tex])
Solving (a): Area of the flag as a sum of each section
We simply calculate the area of each section.
[tex]Area = Length * Width[/tex]
For the green section;
[tex]Area = x * 2[/tex]
[tex]Area = 2x[/tex]
For the orange section
[tex]Area = 2 * 1\frac{1}{2}[/tex]
[tex]Area = 3[/tex]
For the purple section
[tex]Area = 3 * (x + 1\frac{1}{2})[/tex]
[tex]Area = 3 * (x + \frac{3}{2})[/tex]
[tex]Area = 3x + \frac{9}{2}[/tex]
Total Area = Sum of the above areas
[tex]Area = 2x + 3 + 3x + \frac{9}{2}[/tex]
Collect Like Terms
[tex]Area = 2x + 3x+ 3 + \frac{9}{2}\\[/tex]
[tex]Area = 5x+ \frac{6+9}{2}[/tex]
[tex]Area = 5x+ \frac{15}{2}[/tex]
[tex]Area =\frac{10x + 15}{2}[/tex]
Solving (b): Area of the flag as a product
From the attachment,
[tex]Length = 2 + 3[/tex]
[tex]Length = 5[/tex]
[tex]Width = x + 1\frac{1}{2}[/tex]
[tex]Area = Length * Width[/tex]
[tex]Area = 5(x + 1\frac{1}{2})[/tex]
[tex]Area = 5(x + \frac{3}{2})[/tex]
[tex]Area = 5x + \frac{15}{2}[/tex]
Take LCM
[tex]Area = \frac{10x + 15}{2}[/tex]
