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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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