Trapezium cross-section — solve for depth from area and widths: A canal cross-section is a trapezium. The top width is 10 m, the bottom width is 6 m, and the cross-sectional area is 640 sq m. Find the depth (perpendicular distance between the parallel sides).

Introduction / Context:For a trapezium, area = (1/2) * (sum of parallel sides) * height. Here height is the canal depth.

Given Data / Assumptions:

• a = 10 m (top width)
• b = 6 m (bottom width)
• Area = 640 sq m

Concept / Approach:Let depth = h. Then 640 = (1/2) * (10 + 6) * h = 8h. Solve for h.

Step-by-Step Solution:8h = 640 ⇒ h = 80 m

Verification / Alternative check:Back-substitute: (1/2)*(16)*80 = 640 ✓

Why Other Options Are Wrong:40 m gives half the area; 160 m doubles the area; 384 m is unrelated.

Common Pitfalls:Using difference of widths instead of sum; forgetting the 1/2 factor.

Final Answer:80 meters