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Largest Area?

Source: 1981 National High School Mathematics League, Problem 4

February 20, 2020

Problem Statement

In the four figures, which one has the largest area? (A)△ABC:∠A=π3,∠B=π4,∣AC∣=2\text{(A)}\triangle ABC: \angle A=\frac{\pi}{3},\angle B=\frac{\pi}{4},|AC|=\sqrt2 (B)\text{(B)}trapezium: two diagonals are 2\sqrt2 and 3\sqrt3, intersection angle is 5π12\frac{5\pi}{12}. (C)\text{(C)}Circle: with a radius of 11. (D)\text{(D)}Square: the length of a diagonal is 2.52.5.
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