To find the area of a parallelogram, we can use the formula:
Area = base × height
However, since we have the lengths of the sides and the angle between them, we can also apply the formula:
Area = a × b × sin(θ)
Where:
- a = length of one side (6 units)
- b = length of the adjacent side (12 units)
- θ = angle between the two sides (60°)
Now, plugging in the values, we get:
Area = 6 × 12 × sin(60°)
We know that sin(60°) = √3/2. Substituting this value into our equation gives:
Area = 6 × 12 × (√3/2)
Area = 72 × (√3/2)
Area = 36√3 square units.
Thus, the area of the parallelogram is approximately 62.35 square units, when we calculate 36 times the approximate value of √3 (which is about 1.732).