Question

Which expressions represent the area of the entire shaded region, including the light and dark shading? select three options. 12a cm2 2b cm2 (6a – b) cm2 (12a 2b) cm2 (6a b) cm2

Answer 1

A triangle is a polygon. The total area of the figure can be represented by 12a, (6a+b), and 2b cm².

What is a triangle?

A triangle is a polygon with 3 sides and 3 vertices.

Since the area of a single triangle is a cm², and the shape is formed of 12 triangles, therefore, the area of the 12 triangles will be equal to,

$\text{Area of the complete figure} = 12 \times a = 12a\rm \ cm^2$

Given that the area of the complete dark portion is b cm², therefore, the area of the 6 triangles with a cm² of area each, and the black portion can be written as,

$\text{Area of the complete figure} = (6 \times a)+b = (6a+b)\rm \ cm^2$

As the dark portion also consists of 6 triangles with an area of a cm² each and the total sum of this dark area is b cm². Also, the light portion consists of 6 triangles with an area of a cm². Therefore, the total area can be written as,

$\text{Total area} = 6a+6a = b+b = 2b\rm\ cm^2$

Thus, the total area of the figure can be represented by 12a, (6a+b), and 2b cm².

Learn more about Triangles:

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