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The fraction of the image in blue with respect to the <em>entire</em> hexagon is .
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:
(1)
Where:
- Area of a type-1 triangle.
- Area of a type-2 triangle.
The formulae for the area of the shaded region () and the <em>entire</em> hexagon (
) are, respectively:
(2)
(3)
And the fraction of the image in blue is:
The fraction of the image in blue with respect to the <em>entire</em> hexagon is .
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Answer:
Dimension: 2inches by 4 inches
Step-by-step explanation:
Given
Required
Determine the dimension.
This is calculated as :
So:
Substitute 72 for A
Divide bith sodes by 2
Take square root of both sides
Recall that:
Hence:
Hence, the dimension is: 2 by 3 inches