Area of a rhombus from its diagonals Find the area (in cm²) of a rhombus whose diagonals are 25 cm and 20 cm.
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A500
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B250
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C125
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D200
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ENone of these
Answer
Correct Answer: 250
Explanation
Introduction / Context:Rhombus area equals half the product of its diagonals—one of the most direct area formulas for this quadrilateral. This avoids computing side or height.
Given Data / Assumptions:
- d1 = 25 cm
- d2 = 20 cm
Concept / Approach:Area = (d1 * d2) / 2. Substitute and compute exactly; no trigonometry is needed.
Step-by-Step Solution:
Area = (25 * 20)/2 = 500/2 = 250 cm^2Verification / Alternative check:If needed, one can confirm by splitting the rhombus into four right triangles formed by the diagonals (which are perpendicular), summing their areas.
Why Other Options Are Wrong:500 doubles the correct area; 125 halves it; 200 is unrelated to (d1 * d2)/2 here.
Common Pitfalls:Forgetting the 1/2 factor is the most common mistake with this formula.
Final Answer:250