Geometry

General Polygons

General Polygons - Area

         

What is the area of the shaded hexagon in rectangle ABCDABCD in the diagram below?

Details and assumptions:

  • If your answer is 12 cm212 \text{ cm}^2, type it in as 1212.

What is the area of hexagon ABCDEFABCDEF in the diagram below?

Details and assumptions:

  • Let 3=1.732.\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 ABCDABCD in the diagram below?

Details and assumptions:

  • Let 3=1.732.\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 sin15:\sin 15^\circ : sin215=1cos302.\sin^2 15^\circ = \dfrac {1-\cos 30^\circ}{2}.
  • Let 2=1.414,\sqrt{2}=1.414, 3=1.732,\sqrt{3}=1.732, and 6=2.449.\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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