How do you calculate the area of a parallelogram with sides measuring 6 and 12 units and an angle of 60 degrees?

To find the area of a parallelogram, you can use the formula:

Area = base × height

However, when you only know the lengths of the sides and the angle between them, the formula can be adjusted. The area can also be calculated using:

Area = a × b × sin(θ)

Where:

  • a and b are the lengths of the sides.
  • θ is the angle between these sides.

In this case, you have:

  • a = 6
  • b = 12
  • θ = 60 degrees

Now, plug the values into the formula:

Area = 6 × 12 × sin(60)

The sine of 60 degrees is approximately 0.866 (or you can use the exact value, which is √3/2). So:

Area = 6 × 12 × 0.866

Calculating this gives:

Area ≈ 6 × 12 × 0.866 = 62.32

Thus, the area of the parallelogram is approximately 62.32 square units.

Leave a Comment