Question

Someone please help I don’t understand this please

Answer 1

The fraction of the image in blue with respect to the entire hexagon is $\frac{1}{3}$.

Estimation of the ratio of the shaded region area to the entire area

Initially we proceed to create auxiliar constructions , represented by red line segments, to re-define the hexagon as a sum of standard figures. According to the figure, we find two types of triangles (type-1 and type-2), and the following relationship between the two types:

$A_{1} = A_{2}$ (1)

Where:

• $A_{1}$ - Area of a type-1 triangle.
• $A_{2}$ - Area of a type-2 triangle.

The formulae for the area of the shaded region ($A_{s}$) and the entire hexagon ($A_{h}$) are, respectively:

Shaded region

$A_{s} = 2\cdot A_{1} + 4\cdot A_{2}$ (2)

Entire hexagon

$A_{h} = 8\cdot A_{1} + 10\cdot A_{2}$ (3)

And the fraction of the image in blue is:

$\frac{A_{s}}{A_{h}} = \frac{2\cdot A_{1}+4\cdot A_{2}}{8\cdot A_{1}+10\cdot A_{2}}$

$\frac{A_{s}}{A_{h}} = \frac{6\cdot A}{18\cdot A}$

$\frac{A_{s}}{A_{h}} = \frac{1}{3}$

The fraction of the image in blue with respect to the entire hexagon is $\frac{1}{3}$. $\blacksquare$

To learn more on hexagons, we kindly invite to check this verified question: brainly.com/question/4083236