A triangle is a polygon. The total area of the figure can be represented by 12a, (6a+b), and 2b cm².
<h3>What is a triangle?</h3>
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](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20the%20complete%20figure%7D%20%3D%2012%20%5Ctimes%20a%20%3D%2012a%5Crm%20%5C%20cm%5E2)
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](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20the%20complete%20figure%7D%20%3D%20%286%20%5Ctimes%20a%29%2Bb%20%3D%20%286a%2Bb%29%5Crm%20%5C%20cm%5E2)
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](https://tex.z-dn.net/?f=%5Ctext%7BTotal%20area%7D%20%3D%206a%2B6a%20%3D%20b%2Bb%20%3D%202b%5Crm%5C%20cm%5E2)
Thus, the total area of the figure can be represented by 12a, (6a+b), and 2b cm².
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brainly.com/question/2773823