Points M, N, and O are the midpoints of sides KL, LJ, and JK, respectively, of triangle JKL. Points P, Q, and R are the midpoints of NO, OM, and MN, respectively. If the area of triangle PQR is 12, then what is the area of triangle JQR?
Let's denote the area of triangle JKL as A.
Since M, N, and O are midpoints, we know that the area of triangle JMN is A/4, the area of triangle MON is A/4, and the area of triangle KNO is A/4.
Therefore, the area of triangle NOJ is A/2, and since P is the midpoint of NO, the area of triangle JOP is A/4.
Similarly, we can deduce that the area of triangle JQO is A/8 and the area of triangle JQR is A/16.
Since the area of triangle PQR is 12, we have:
A/16 = 12
A = 192
Therefore, the area of triangle JQR is 192/16 = 12.
Hence, the area of triangle JQR is 12.