Each of two angles of a triangle is 60° and the included side is 4 inches. The area of the triangle, in square inches, is:

1960 AMC 12 Problem 4

Attempt Problem 4 of the 1960 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1960 AMC 12 solutions, or check the answer key.

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Each of two angles of a triangle is

60^\circ

and the included side is

4

inches. The area of the triangle, in square inches, is:

8\sqrt3

8

4\sqrt3

4

2\sqrt3

Determine the third angle of the triangle

Use the area formula for an equilateral triangle of side

4

The third angle is also

60^\circ,

so the triangle is equilateral with side

4.

Its area is

\frac{\sqrt3}{4}(4)^2=4\sqrt3.

Thus, the correct answer is C.