A piece of art is in the shape of an equilateral triangle with sides of 6 in. Find the area of the piece of art. Round your answer to the nearest tenth.

Question

psymon · Answer

Triangle area = (1/2)base x height. We have a base of 6 inches, but we don't have a height, so we need to get that:

psymon · Answer

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The height is the base to the highest point of the triangle. We can draw an imaginary line straight through the middle to help us find the height. Now when I draw that imaginary line, I have split the base of the triangle in half as well, each half having a length of 3. Now that I have this, I can find the height by pythagorean theorem. If you recall, pythagorean theorem is:
$$a ^{2}+b ^{2}= c ^{2}$$where c is the hypotenuse (longest side)