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?

Answer 1

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.