The diagonal of a square is equal to the smaller diagonal of a rhombus with an angle of 60

The diagonal of a square is equal to the smaller diagonal of a rhombus with an angle of 60 degrees and a side of 3√2. Find the area of the square.

To solve this task, you need to find the value of the area of the square;
Consider this task and analyze it;

According to the condition of the task, we are given a square whose diagonal is equal to the smaller diagonal of a rhombus with an angle of sixty degrees.

Let’s write the formula for the area of a square in terms of its diagonal;

S = 1/2 * d², where d is the diagonal of the square;

Find the diagonal of the square;

Since the angle of the rhombus is 60 °, it means that the triangle with this angle is equilateral, which means that all sides are equal to 3√2;

Substitute in the formula and get;

S = 1/2 * (3 * √2) 2;

S = 1/2 * 9 * 2;

S = 9cm2.