One of the corners of the rhombus is 2 times larger than the other, and its side is 6 cm. Find the area of the rhombus.

1. Let us denote the degree measure of the smaller angle of the rhombus through xy

2. Define the degree measure of the larger angle of the rhombus:

2 * x = 2x.

3. Let’s compose and solve the equation:

2x + x = 180˚;

3x = 180˚;

x = 180˚: 3;

x = 60˚.

4. The degree measure of the smaller angle of the rhombus is x = 60˚.

5. What is the degree measure of the larger angle of the rhombus?

180˚ – 60˚ = 120˚.

6. What is the area of the rhombus?

6 ^ 2 * sin60˚ = 36 * √3 / 2 = 18√3 (cm ^ 2)

Answer: the area of a rhombus is 18√3 cm ^ 2.