To find the area of a rhombus when the lengths of the sides and one of the angles are known, you can use the formula:
Area = a² × sin(θ)
where a is the length of a side, and θ is the angle between two sides.
In this case, we have:
- Length of a side (a) = 6 inches
- Angle (θ) = 60 degrees
First, we need to calculate sin(60°). The sine of 60 degrees is a well-known value:
sin(60°) = √3 / 2
Now, we can substitute the values into the area formula:
Area = 6² × sin(60°)
Area = 36 × (√3 / 2)
Area = 36 × 0.866 = 31.104
Therefore, the area of the rhombus is approximately 31.1 square inches.