# The sides of such triangles are 2/1, and the area of the larger one is 36. find the area of the smaller triangle.

The area of ​​arbitrary, larger and smaller, triangles is calculated by the formulas:
Sb = ½ * A * B * sinα;
Sm = ½ * a * b * sinα,
where A and B are the sides of the larger triangle, a and b are the sides of the smaller triangle, α is the angle between the corresponding sides of the larger and smaller triangles, in similar triangles these angles are equal.
Using the property of similar triangles, we write:
A: a = 2: 1.
B: b = 2: 1.
Therefore, A = 2 * a, B = 2 * b.
Let’s find the area ratio:
Sb / Sm = (½ * A * B * sinα) / (½ * a * b * sinα) = (A * B) / (a ​​* b) = (2 * a * 2 * b) / (a ​​* b ) = 4.
Hence,
36 / Sм = 4.
Sм = 9.
The area of ​​the smaller triangle is 9.

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