A rhombus has a 26 m side and a 20 m diagonal. What is its area_______?
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Answer: D. 480 sq m
Explanation
Using the geometric properties of a rhombus, the side length and half-diagonals form a right-angled triangle. Applying the Pythagorean theorem allows calculation of the unknown half-diagonal, yielding a full second diagonal of 48 meters. Multiplying one-half of the product of both diagonal lengths results in an area of exactly 480 square meters. The diagonals of a rhombus always intersect each other at right angles and bisect one another equally. The area of any rhombus can be calculated as one-half of the product of its two diagonal lengths. All four sides of a rhombus are equal in length by definition.
Option A is incorrect because it uses an improper formula that does not match the diagonal area calculation. Option B underestimates the area by failing to correctly determine the full length of the second diagonal. Option C represents a calculation error resulting from improper application of the Pythagorean right triangle theorem.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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