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General Polygons

Convex and concave, regular and irregular, similar and congruent – learn every variety of polygon you can encounter.

Area

         

What is the area of the shaded hexagon in rectangle \(ABCD\) in the diagram below?

Details and assumptions:

  • If your answer is \(12 \text{ cm}^2\), type it in as \(12\).

What is the area of hexagon \(ABCDEF\) in the diagram below?

\[\] Details and assumptions:

  • Let \(\sqrt{3}=1.732.\)
  • In the diagram above, red lines are parallel to one another and blue lines are parallel to one another.

What is the area of quadrilateral \(ABCD\) in the diagram below?

\[\] Details and assumptions:

  • Let \(\sqrt{3}=1.732.\)

What is the area of the nonagon inscribed in the circle with radius 4 below?

\[\] Details and assumptions:

  • Use the following formula to find \(\sin 15^\circ :\) \[\sin^2 15^\circ = \dfrac {1-\cos 30^\circ}{2}.\]
  • Let \(\sqrt{2}=1.414,\) \(\sqrt{3}=1.732,\) and \(\sqrt{6}=2.449.\)

What is the area of the regular hexagon below, where the area of the shaded region is 34?

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