# geometry

find the area of an equilateral triangle with sides measuring 6 meters.

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1. base x height/2

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2. when an equilateral triangle is cut in half, the two triangles formed are 30-60-90 triangles, whose shorter side (not the one going through the main triangle) is one half the side. in 30-60-90 triangles, the hypotenuse is double the shorter leg, and the longer leg is the shorter leg times the square root of three. you could also do this with the pythagorean theorum... 6squared - 3squared=xsquared... solve for x. The height of the triangle ends up as square root of 27 (3radical3). Area of triangle = 1/2 b h where b is the base and h is the height. in this case the base is 6 and the height, as calculated, is 3radical3. multiply it out, and the answer is 9radical3 or about 15.6

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3. cute

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