Question

PLEASE HELP ASAP! VERY DESPERATE
Michelle is making a poster for a class presentation. She plans to have four sections of information, each with a different background color. The diagram shows the lengths and widths of each section, where a is the length of the red section. Which expression for the area of the poster is written as the sum of the areas of each colored section? (answer choices are in the screenshot provided. thanks! <3)

Answer 1

Answer:

first option

Step-by-step explanation:

the area of a rectangle is

base*height

$Purple=(3)\times(a)\\\\=3a\\\\\\Green=(\frac{1}{2})\times(3)\\\\=\frac{3}{2}\\\\\\Red=1\times a\\\\=a\\\\\\Yellow=\frac{1}{2}\times 1\\\\=\frac{1}{2}$

so the sum is

$\Sigma A=3a+a+\frac{3}{2}+\frac{1}{2}$

which is the first option

Answer 2

The expression for the area of the poster is written as the sum of the areas of each colored section is 3a + a + 3 1/2 + 1/2

Area of a rectangle = length × width

Purple color:

Area = length × width

= 3 × a

= 3a

Red color:

Area = length × width

= 1 × a

= a

Green color:

Area = length × width

= 3 × 1/2

= 3 1/2

Yellow color:

Area = length × width

= 1 × 1/2

= 1/2

Sum of the areas = purple + red + green + yellow

= 3a + a + 3 1/2 + 1/2

Therefore, expression for the area of the poster is written as the sum of the areas of each colored section is 3a + a + 3 1/2 + 1/2

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