The continuation of the lateral sides AB and CD of trapezoid ABCD intersect at point M. Find the area of the trapezoid

The continuation of the lateral sides AB and CD of trapezoid ABCD intersect at point M. Find the area of the trapezoid if BC: AD = 2: 5 and the area of triangle BMC is 12 cm ^ 2.

Triangles AMD and BMC are similar since angle MBC = angle MAD and angle MCB = angle MDA are respectively, and angle M is common.
Hence, the ratio of BC to AD is a similarity factor of 2/5 (we get the ratio of the sides of the smaller triangle to the large triangle)
The ratio of the areas of triangles BCM and AMD is equal to the square of the coefficient of similarity = 4/25
In order to find the area of ​​the larger triangle, let’s draw up a proportion, where the square of the similarity coefficient will be equal to the ratio of the areas: 4/25 = 12 / x
x = (12 * 25) / 4 = 75 is the area of ​​the AMD triangle.
Now, to find the area of ​​the trapezoid, subtract the area of ​​the small triangle from the area of ​​the large triangle: 75-12 = 63
Answer: 63