What is the area of the equilateral triangle with side length of 6?

The area is about 15.59 and is round to the nearest hundredth.

Step-by-step explanation:

An equilateral triangle has three equal sides is just like an isosceles triangle.

So in this case, we know that the base is 6 and since the base is 6 all the other two sides is also 6 .But we do not know the height to find the area so we need to find the height.

The height is the distance of from the base to the tip or top which helps form two right triangles.. And if you divide as  an equilateral triangle into two parts you will form two right triangles. Imagine we have divide the isosceles triangle into two parts to form two right triangles. We will now have a base of 3 instead of 6 and and hypotenuse of 6 .  but we still don't know the height so we need to  find it.

Using the Pythagorean Theorem we could say that a^2 plus b^2 squared is equal to c^2 squared.

We know a as 3 and c the hypotenuse as 6.

so 3^2 + b^2 =6^2  solve for b

  9 + b^2 = 36

 -9               -9

   b^2 = 27

  b=  

b= 5.196  

Now we know that b is about 5.196 which is the  height.Now we could find the area by  multiplying  the base by the height.

5.196 * 6 = 31.176  

31.176/2 = 15.588  

Now you could round it to the nearest hundredth to be 15.59  

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step-by-step explanation: