Parallelogram with sides 30 m and 14 m, diagonal 40 m: Find the area of the parallelogram.

Introduction / Context:For a parallelogram, area = a*b*sin(θ). A diagonal along with side lengths can determine the included angle using the cosine rule for parallelogram diagonals.

Given Data / Assumptions:

• Sides a = 30 m, b = 14 m.
• One diagonal d = 40 m.

Concept / Approach:Diagonal formula: d^2 = a^2 + b^2 + 2ab*cosθ. Solve for cosθ, then compute sinθ and area = a*b*sinθ.

Step-by-Step Solution:

Verification / Alternative check:Use identity d1^2 + d2^2 = 2(a^2 + b^2) to cross-check angle consistency (optional).

Why Other Options Are Wrong:136, 236, 436 do not match the area from the uniquely determined angle.

Common Pitfalls:Using 0.5*a*b*sinθ (triangle formula) by mistake; a parallelogram’s area is a*b*sinθ.

Final Answer:336