Mark M. answered • 06/10/16

Mathematics Teacher - NCLB Highly Qualified

The height divides the triangle into two 30-60-90 triangles.

The height is √3 / 2 times the side (hypotenuse), or x√3 /2.

The area of the triangle is (1/2)(x)(x√3/2), or x

^{2}√3/4.Amy S.

I mean x√3/2

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06/10/16

Mark M.

tutor

In a 30-60-90 triangle, the side opposite the 30° angle is one-half of the hypotenuse.

The side opposite the 60° is √3/2 of the hypotenuse.

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06/10/16

Amy S.

If you don't mind, could you show me your full working?

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06/10/16

Mark M.

tutor

Draw and equilateral triangle. Label each side "x."

Draw an altitude from the base to the opposite vertex. Label it "a."

You now have two triangles each a 30-60-90 triangle.

The side "x" is the hypotenuse. One-half of the base is the short leg.

The altitude is the long leg.

By Pythagoras:

x

^{2}= (x/2)^{2}+ a^{2}x

^{2}= x^{2}/4 + a^{2}x

^{2}- x^{2}/4 = a^{2}3x

^{2}/4 = a^{2}x√3 / 2 = a

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06/10/16

Amy S.

^{2}√3/2?06/10/16