Question 562459
have an equilateral triangle with sides of 13 in.  How do I find the area?  I know formula is A=1/2bh.  Base is 13 but what is height?
<pre>
Draw it:

{{{drawing(400,1882/5,-.5,2.5,-.5, 2.232,
locate(.3,.9,13), locate(1,-.06,13),locate(1.6,.9,13),

triangle(0,0,2,0,1,sqrt(3)) )}}}

Draw the height (in green), which will divide the bottom
13 in. bottom side into two 6.5 in. parts:

{{{drawing(400,1882/5,-.5,2.5,-.5, 2.232,
green(line(1,0,1,sqrt(3))), locate(1.05,.8,h),
locate(.3,.9,13), locate(.4,-.06,6.5),locate(1.6,.9,13),
locate(1.4,-.06,6.5),


triangle(0,0,2,0,1,sqrt(3)) )}}}


If we look at only the left half of the triangle, we
see that it is a right triangle:

{{{drawing(400,1882/5,-.5,2.5,-.5, 2.232,
green(line(1,0,1,sqrt(3))), locate(1.05,.8,h),
locate(.3,.9,13), locate(.4,-.06,6.5),
triangle(0,0,1,sqrt(3),0,0),

triangle(0,0,1,0,1,0) )}}}

The Pythagorean theorem applies to right triangles
and says that

 6.5² + h² = 13²
42.25 + h² = 169  
        h² = 126.75
         h = {{{sqrt(126.75)}}}
         h = 11.25833025     

Now use the formula:

   A = {{{1/2}}}bh
   A = {{{1/2}}}(6.5)(11.24833025)
   A = 36.58957331 square inches

Edwin</pre>