Find the area of a rhombus if its vertices taken in order are (3, 0), (4, 5), (-1, 4), and (-2, -1).
Answer and explanation
Correct answer: C. 24 square units
- Step 1: Diagonals of rhombus connect opposite vertices: d1 between (3, 0) and (-1, 4), d2 between (4, 5) and (-2, -1).
- Step 2: d1 = sqrt((-1 - 3)^2 + (4 - 0)^2) = sqrt(16 + 16) = sqrt(32) = 4√2.
- Step 3: d2 = sqrt((-2 - 4)^2 + (-1 - 5)^2) = sqrt(36 + 36) = sqrt(72) = 6√2.
- Step 4: Area = (1/2) d1 d2 = (1/2) (4√2) (6√2) = (1/2) 24 2 = 24 square units.
Why not the others: 20 square units, 28 square units and 32 square units do not fit.
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