In a rectangle ABCD AB = 12cm. Point M belongs to side BC, MC = 6cm, AM = 15cm. Find the area of a rectangle.

Since point M belongs to side BC, we get a right-angled triangle ABM with sides AB = 12 cm and AM = 15 cm;

By the Pythagorean theorem, we get the expression:

(BM) ^ 2 = (AM) ^ 2 – (AB) ^ 2 = (15) ^ 2 – (12) ^ 2 = 225 – 144 = 81 = (9) 2;

Thus, the side of the BM is 9 cm;

Next, we find out the length of the side of the aircraft:

BC = BM + MC = 9 + 6 = 15 cm;

And finally, the area of the rectangle ABCD:

S = 15 * 12 = 180 cm.

Answer: the area of the rectangle ABCD is 180 cm.