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

2 answers

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:12a cm2
2b cm2
(6a + b) cm2Step-by-step explanation:The complete question isThe 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) cm2The picture of the question in the attached figurewe know thatThe area of the entire shaded region is equal to the area of the the light and dark shadingsostep 1Find the area of the light shadingThe area is equal to the area of six congruent equilateral triangles[tex]A_1=6a\ cm^2[/tex]step 2Find the area of the dark shadingThe area is equal to the area of the regular hexagon[tex]A_2=b\ cm^2[/tex]step 31) Find the total area[tex]A=A_1+A_2=(6a+b)\ cm^2[/tex]2) Remember that the figure consists of 12 congruent equilateral trianglesso[tex]A=12a\ cm^2[/tex]3) The area of the light shading is the same that the area of the dark shadingso6a=btherefore[tex]A=2b\ cm^2[/tex]

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