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MAXImum [283]
2 years ago
9

Someone please help I don’t understand this please

Mathematics
1 answer:
sdas [7]2 years ago
6 0

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

<h3>Estimation of the ratio of the shaded region area to the entire area</h3>

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 <em>entire</em> hexagon (A_{h}) are, respectively:

<h3>Shaded region</h3>

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

<h3>Entire hexagon</h3>

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 <em>entire</em> hexagon is \frac{1}{3}. \blacksquare

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

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