Question 706561
<pre>
It can be worked if the triangle on the left is isosceles,
like this:



{{{drawing(400,5200/27,-2,25,-2,11, locate(4,0,8),locate(15,0,15),
locate(.5,4.7,10),arc(0,0,3,-3,0,65),arc(8,0,3,-3,115,180),
triangle(0,0,8,0,4,sqrt(84)), triangle(23,0,8,0,4,sqrt(84)) )}}} {{{matrix(6,1,

or, a, right,triangle,like,"this-->")}}} {{{drawing(400,5200/27,-2,25,-2,11,
locate(2.4,3.5,10),locate(4,0,8),locate(15,0,15),rectangle(7.5,0,8,.5),
triangle(0,0,8,0,8,6), triangle(23,0,8,0,8,6) )}}}

If it's the first case, we draw the height, h, or altitude (in green), and
dividing the 8 base into two segments 4 each

{{{drawing(400,5200/27,-2,25,-2,11, locate(2,0,4)locate(5,0,4),locate(15,0,15),
locate(.5,4.7,10),arc(0,0,3,-3,0,65),arc(8,0,3,-3,115,180),
green(line(4,0,4,sqrt(84))),locate(4.2,4.7,h),
triangle(0,0,8,0,4,sqrt(84)), triangle(23,0,8,0,4,sqrt(84)) )}}} {{{matrix(12,1,

or, in, the, other, case, the, height,h,is,the,vertical,"line-->")}}}  {{{drawing(400,5200/27,-2,25,-2,11, locate(8.2,3.5,h),
locate(2.4,3.5,10),locate(4,0,8),locate(15,0,15),rectangle(7.5,0,8,.5),
triangle(0,0,8,0,8,6), triangle(23,0,8,0,8,6) )}}}

In either case we use the Pythagorean theorem to get the height h

4˛ + h˛ = 10˛                                 8˛ + h˛ = 10˛
16 + h˛ = 100                                 64 + h˛ = 100
     h˛ = 84                                       h˛ = 36
      h = &#8730;<span style="text-decoration: overline">84</span>                                       h = &#8730;<span style="text-decoration: overline">36</span>
      h = &#8730;<span style="text-decoration: overline">4*21</span>                                     h = 6
      h = 2&#8730;<span style="text-decoration: overline">21</span>

The formula for the area of a triangle is A = {{{1/2}}}base×height

We have the base in both cases as 8+15 or 23.

The case on the left is 

A = {{{1/2}}}(23)2&#8730;<span style="text-decoration: overline">21</span>
  = 23&#8730;<span style="text-decoration: overline">21</span>
  = 105.4 square meters, approximately

On the right,

A = {{{1/2}}}(23)(6) 
  = 69 square meters

Edwin</pre>