Question

Which expressions represent the area of the entire shaded

region, including the light and dark shading? Select three
options.
12a cm2
2b cm
(6a - b) cm
(12a + 2b) cm
(6a + b) cm

Answer 1

Answer: 1 2 5

Explanation:

Answer 2

12a cm2

2b cm2

(6a + b) cm2

Explanation:

The complete question is

The figure consists of 12 congruent equilateral triangles. The area of one equilateral triangle is a cm2. The area of the hexagon, shaded slightly darker, is b cm2.

Which expressions represent the area of the entire shaded region, including the light and dark shading? Check all that apply.

12a cm2

2b cm2

(6a - b) cm2

(12a + 2b) cm2

(6a + b) cm2

The picture of the question in the attached figure

we know that

The area of the entire shaded region is equal to the area of the the light and dark shading

so

step 1

Find the area of the light shading

The area is equal to the area of six congruent equilateral triangles

`A_1=6a\ cm^2`

step 2

Find the area of the dark shading

The area is equal to the area of the regular hexagon

`A_2=b\ cm^2`

step 3

1) Find the total area

`A=A_1+A_2=(6a+b)\ cm^2`

2) Remember that the figure consists of 12 congruent equilateral triangles

so

`A=12a\ cm^2`

3) The area of the light shading is the same that the area of the dark shading

so

6a=b

therefore

`A=2b\ cm^2`