Find the area of a rhombus with a side of 12 cm and an angle of 60 °.

In the condition, we are given a rhombus with a side of 12 cm and an acute angle of 60 °. In order to find the area of a rhombus, let’s recall the formula for finding the area through the side of a rhombus and the angle between them.

So, the formula for finding the area looks like this:

S = a ^ 2 * sin a.

The area of the rhombus is equal to the product of the sides and the sine of the angle between them.

We know the sides of the rhombus and the angle between them. It remains only to substitute and perform calculations:

S = a ^ 2 * sin a = 12 ^ 2 * Sin 60 ° = 144 * √3 / 2 = 72√3 cm2.

Answer: the area of the rhombus is 72√3 cm2.