Consider the diagram showing the path Joel biked. Joel biked 9 miles east and then 12 miles north. If he biked back to his start
ing point using the most direct route, how many miles would he ride all together? Joel’s starting point is x
2 answers:
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Answer:
The approximate are of the inscribed disk using the regular hexagon is
Step-by-step explanation:
we know that
we can divide the regular hexagon into 6 identical equilateral triangles
see the attached figure to better understand the problem
The approximate area of the circle is approximately the area of the six equilateral triangles
Remember that
In an equilateral triangle the interior measurement of each angle is 60 degrees
We take one triangle OAB, with O as the centre of the hexagon or circle, and AB as one side of the regular hexagon
Let
M ----> the mid-point of AB
OM ----> the perpendicular bisector of AB
x ----> the measure of angle AOM
In the right triangle OAM
so
we have
substitute
Find the area of six equilateral triangles
simplify
we have
substitute
Therefore
The approximate are of the inscribed disk using the regular hexagon is
