General Polygons

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 OO has point XX and point YY on its circumference. If the radius of the circle is 6 and the measure of XYXY is 10, what is the area of XOY?\triangle{XOY}?

The ratio of acute angle AA to acute angle BB is 7 to 4. The complement of one angle is 1515^\circ larger than the complement of the other. What is A+B?A + B?

The diagonals of rectangle ABCDABCD meet at point X.X. DXC=120.\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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