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# General Polygons

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

# General Polygons - 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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