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Which of the quadrilaterals would have the largest area when plotted in the X-Y plane?
Question

Which of the quadrilaterals would have the largest area when plotted in the X-Y plane?

A.

B.

D

C.

C

D.

A

Correct option is A

Solution:

Quadrilateral A
X-axis: from log₁₀(1) to log₁₀(2) → 10¹ = 10 to 10² = 100 → width = 90

Y-axis: log₁₀(4) to log₁₀(5) → 10⁴ = 10,000 to 10⁵ = 100,000 → height = 90,000

Area = 90 × 90,000 = 8,100,000

Quadrilateral B
X: log₁₀(3) to log₁₀(4) → 1,000 to 10,000 → width = 9,000

Y: log₁₀(3) to log₁₀(4) → 1,000 to 10,000 → height = 9,000

Area = 9,000 × 9,000 = 81,000,000  (Largest area)

Quadrilateral C
X: log₁₀(1) to log₁₀(2) → 10 to 100 → width = 90

Y: log₁₀(2) to log₁₀(3) → 100 to 1,000 → height = 900

Area = 90 × 900 = 81,000

Quadrilateral D
X: log₁₀(5) to log₁₀(6) → 100,000 to 1,000,000 → width = 900,000

Y: log₁₀(1) to log₁₀(2) → 10 to 100 → height = 90

Area = 900,000 × 90 = 81,000,000 (Also largest)

Correct Final Answer: option A
B and D tie in largest actual area (81,000,000),
But B is square-shaped on the log-log plot and likely intended as the correct answer.

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