2024 AMC 12A Problem 20

Points P and Q are chosen uniformly and independently at random on sides \overline {AB} and \overline{AC}, respectively, of equilateral triangle \Delta ABC. Which of the following intervals contains the probability that the area of \triangle APQ is less than half the area of \triangle ABC?

\textbf{(A) } \left[\frac 38, \frac 12\right] \qquad \textbf{(B) } \left(\frac 12, \frac 23\right] \qquad \textbf{(C) } \left(\frac 23, \frac 34\right] \qquad \textbf{(D) } \left(\frac 34, \frac 78\right] \qquad \textbf{(E) } \left(\frac 78, 1\right]

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.