ABCD is a parallelogram. P is the midpoint of AB, Q is the midpoint of BC, R is the midpoint of CD and S is the midpoint of AD. Lines AQ, CS, BR and DP, when intersecting with each other, make a new parallelogram. Find the ratio of the area of that parallelogram and the area of ABCD.
P.S. I'm assuming I need to introduce variables for two sides of the parallelogram (e.g. a for AB and DC, and b for BC and AD) and maybe α for the angle BAD, and thus say that the area of ABCD is ab*sin(α), but I'm not sure how to get the other parallelogram's area (fyi, I named it A1B1C1D1).
P.S. I'm assuming I need to introduce variables for two sides of the parallelogram (e.g. a for AB and DC, and b for BC and AD) and maybe α for the angle BAD, and thus say that the area of ABCD is ab*sin(α), but I'm not sure how to get the other parallelogram's area (fyi, I named it A1B1C1D1).