Question

A school flag consists of three rectangular sections that each have a different color.

Answer 1

Answer:

$Area =\frac{10x + 15}{2}$ 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 $1\frac{1}{2}$

Purple Section: Dimension: 3 by (x + $1\frac{1}{2}$)

Solving (a): Area of the flag as a sum of each section

We simply calculate the area of each section.

$Area = Length * Width$

For the green section;

$Area = x * 2$

$Area = 2x$

For the orange section

$Area = 2 * 1\frac{1}{2}$

$Area = 3$

For the purple section

$Area = 3 * (x + 1\frac{1}{2})$

$Area = 3 * (x + \frac{3}{2})$

$Area = 3x + \frac{9}{2}$

Total Area = Sum of the above areas

$Area = 2x + 3 + 3x + \frac{9}{2}$

Collect Like Terms

$Area = 2x + 3x+ 3 + \frac{9}{2}$

$Area = 5x+ \frac{6+9}{2}$

$Area = 5x+ \frac{15}{2}$

$Area =\frac{10x + 15}{2}$

Solving (b): Area of the flag as a product

From the attachment,

$Length = 2 + 3$

$Length = 5$

$Width = x + 1\frac{1}{2}$

$Area = Length * Width$

$Area = 5(x + 1\frac{1}{2})$

$Area = 5(x + \frac{3}{2})$

$Area = 5x + \frac{15}{2}$

Take LCM

$Area = \frac{10x + 15}{2}$