Parallelogram area from sides and included angle: The adjacent sides of a parallelogram are 6 cm and 4 cm, and the included angle is 30°. Find its area.

Introduction / Context:
The area of a parallelogram equals product of adjacent sides times the sine of the included angle.

Given Data / Assumptions:

• a = 6 cm
• b = 4 cm
• θ = 30° with sin 30° = 1/2

Concept / Approach:
Area = a * b * sinθ.

Step-by-Step Solution:
Area = 6 * 4 * (1/2) = 12 cm2

Verification / Alternative check:
Units are consistent; the formula directly applies to parallelograms.

Why Other Options Are Wrong:
24 and 48 ignore the sine factor or apply it incorrectly.

Common Pitfalls:
Using cos instead of sin for area or forgetting that 30° has sine 1/2.

Final Answer:
12 cm2