Geometry and TrigonometryMediumArea of a rhombus from its diagonals
Geometry and Trigonometry practice question
A rhombus has diagonals of length 15 and 16. What is the area of the rhombus? (The diagonals of a rhombus are perpendicular and bisect each other.)
Answer: 120
The diagonals cut the rhombus into four right triangles with legs 7.5 and 8. Each has area (1/2)(7.5)(8) = 30, so the rhombus has area 4 × 30 = 120. (Equivalently, area = half the product of the diagonals: (1/2)(15)(16) = 120.)
Common wrong answers
- If you answered 31
- 31 is 15 + 16; area comes from a product, not a sum.
- If you answered 60
- 60 halves the answer again: the four right triangles have area 30 each, and there are four.
- If you answered 240
- 240 is 15 × 16, the full product of the diagonals — that is the area of the rectangle enclosing the rhombus, twice the rhombus itself.
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