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?

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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 \(\triangle{XOY}?\)

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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 \(A + B?\)

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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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