The base of a right prism is a trapezium whose parallel sides are 25 cm and 11 cm and the perpendicular distance between these sides is 16 cm. If the height of the prism is 10 cm, what is the volume of the prism in cubic centimetres?

Introduction / Context:
This question combines area of a trapezium with the concept of volume of a right prism. Once you find the area of the trapezium that forms the base, you simply multiply by the height of the prism to get the volume. It is a straightforward geometric application of well known formulas.

Given Data / Assumptions:
• Base of the prism is a trapezium.
• The two parallel sides are 25 cm and 11 cm long.
• The perpendicular distance (height of the trapezium) between the parallel sides is 16 cm.
• Height of the prism (distance between the two congruent trapezium bases) is 10 cm.
• The prism is right, so lateral edges are perpendicular to the base.

Concept / Approach:
For a trapezium with parallel sides a and b and perpendicular distance h1, the area is:
Area of trapezium = (1/2) × (a + b) × h1.
For a right prism with base area A and height H, the volume is given by:
Volume = A × H.
Thus, compute the trapezium area first, then multiply by the prism height.

Step-by-Step Solution:
Step 1: Let a = 25 cm, b = 11 cm, and h1 = 16 cm. Step 2: Area of trapezium base A = (1/2) × (a + b) × h1. Step 3: Compute a + b = 25 + 11 = 36. Step 4: So A = (1/2) × 36 × 16 = 18 × 16 = 288 sq.cm. Step 5: Height of prism H = 10 cm. Step 6: Volume V = A × H = 288 × 10 = 2880 cubic centimetres.

Verification / Alternative check:
You can double check calculations by recomputing 36 × 16 = 576 and then halving to get 288, confirming the area. Then multiplying by 10 is straightforward. The units also work out correctly: base has sq.cm and multiplying by cm gives cu.cm, as required for volume.

Why Other Options Are Wrong:
• 1440 cu.cm would correspond to using half the correct base area or half the prism height by mistake.
• 1540 cu.cm does not align with any correct combination of the given dimensions.
• 960 cu.cm would come from using 6 instead of 16 as the trapezium height or similar misread data.

Common Pitfalls:
Some learners confuse the trapezium height with the prism height or forget to take the average of the two parallel sides. Carefully distinguishing between the base dimensions and the prism height, and applying the formula exactly, helps avoid these errors.

Final Answer:
The volume of the prism is 2880 cu.cm.