1956 AMC 12 Problem 30

Attempt Problem 30 of the 1956 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 1956 AMC 12 solutions, or check the answer key.

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30.

If the altitude of an equilateral triangle is $\sqrt6,$ then the area is:

$2\sqrt2$

$2\sqrt3$

$3\sqrt3$

$6\sqrt2$

$12$

Answer: B

Concepts:equilateral triangle altitude area

Difficulty rating: 1490

Small Hint:

For side length $s,$ an equilateral triangle has altitude $\frac{s\sqrt3}{2}$

Big Hint:

Once $s$ is known, use area $\frac{sh}{2}$

Solution:

Let the side length be $s.$ From $\frac{s\sqrt3}{2}=\sqrt6,$ we get $s=2\sqrt2.$ Hence the area is $\frac12s\sqrt6 =\frac12(2\sqrt2)(\sqrt6)=2\sqrt3.$

Thus, the correct answer is B.

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