What is the area (in square centimetres) of a rhombus whose diagonals are 25 cm and 20 cm long?

Introduction / Context:
A rhombus is a quadrilateral with all sides equal in length, and its diagonals intersect at right angles and bisect each other. A very useful formula for a rhombus connects its area to the lengths of its diagonals. In many tests, diagonal lengths are given directly, and you are expected to use this relationship to compute the area quickly and accurately.

Given Data / Assumptions:

• We are dealing with a rhombus.
• The diagonals of the rhombus are 25 cm and 20 cm.
• We have to find the area of this rhombus in square centimetres.

Concept / Approach:
The area of a rhombus in terms of its diagonals d1 and d2 is given by:
Area = (d1 * d2) / 2 This formula comes from the fact that the diagonals break the rhombus into four congruent right triangles, and the sum of their areas equals half the product of the diagonals.

Step-by-Step Solution:
Step 1: Identify the diagonals as d1 = 25 cm and d2 = 20 cm. Step 2: Recall the area formula: Area = (d1 * d2) / 2. Step 3: Substitute the given values: Area = (25 * 20) / 2. Step 4: Compute the product 25 * 20 = 500. Step 5: Divide by 2 to get the area: 500 / 2 = 250. Step 6: Therefore, the area of the rhombus is 250 square centimetres.

Verification / Alternative check:
We can also view each diagonal as being split in half by the intersection point, resulting in segments of 12.5 cm and 10 cm. These segments form right triangles with legs 12.5 and 10. The area of one such triangle is (1/2) * 12.5 * 10 = 62.5 sq cm. There are four congruent triangles in the rhombus, so the total area is 4 * 62.5 = 250 sq cm, confirming the earlier result obtained using the formula.

Why Other Options Are Wrong:

• 500: This is the product of the diagonals without dividing by 2, so it doubles the correct area.
• 125 and 200: These might result from miscalculations or using half of one diagonal incorrectly, but they do not satisfy the proper diagonal area formula.
• 300: This is a random distractor that does not correspond to any simple arithmetic based on the given dimensions.

Common Pitfalls:
Learners often confuse the area formula of a rhombus with that of a rectangle and forget to divide by 2. Others may incorrectly add the diagonal lengths or mis-handle the multiplication. Always remember that for a rhombus the area is half the product of the diagonals, not simply the product of side and height unless those are known directly.

Final Answer:
So, the area of the rhombus is 250 sq cm.