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# General Polygons

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

# Geometry Competition Warmup

The area of a right triangle is 30. One of the legs is 2 units more than 2 times the other. What is the hypotenuse of the triangle?

Two equilateral triangles are aligned on top of one another to create a regular hexagon. If the area of the hexagon is 24, what is the area of one of the original equilateral triangles?

Circle $$O$$ has point $$X$$ and point $$Y$$ on its circumference. If the radius of the circle is 6 and the measure of $$XY$$ is 10, what is the area of $$\triangle{XOY}?$$

The ratio of acute angle $$A$$ to acute angle $$B$$ is 7 to 4. The complement of one angle is $$15^\circ$$ larger than the complement of the other. What is $$A + B?$$

The diagonals of rectangle $$ABCD$$ meet at point $$X.$$ $$\angle {DXC} = 120^\circ.$$ If the shorter side of the rectangle measures 4 units, what is the perimeter of the rectangle?

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