Question 1199847
<pre>
What is the area in the figure below, in m^2?
https://imgur.com/a/mBEHVsO

You can use the fact that if the sides of similar triangles are in a certain ratio, then their areas'
ratio  will be the SQUARED VALUES of that ratio. 
Area of larger ΔABC = {{{1/2}}}(AB)(AC) = {{{1/2}}}(7)(24) = 7(12) = 84 m<sup><b>2</sup></b>.
So, shorter leg (ED) of smaller ΔCED to shorter leg of larger ΔABC results in a  {{{4/7}}} ratio. 
Thus, the area of smaller ΔCED will be: {{{highlight_green(matrix(1,11, (4/7)^2, "*", 84, "=", (16/49)(84), "=", "27.42857143,", or, 27.43, m^2, "(approximately)"))}}}
<font color = blue><font size = 4><b>OR</font></font></b>

Larger ΔABC and smaller ΔCED (shaded) are SIMILAR.
Larger ΔABC boasts a 7-24-25 Pythagorean Triple, and AB and AC on larger ΔABC are 7 and 24 m, respectively.
Using triangular similarity (larger ΔABC to smaller ΔCED) theory to find segment EC on smaller ΔCED, we get: {{{matrix(2,3, AB/AC, "=", ED/EC, 7/24, "=", 4/EC)}}}
7EC = 4(24) ---- Cross-multiplying 
{{{matrix(1,6, EC, "=", 4(24)/7, "=", 96/7, m)}}}. With lengths of EC and ED (longer and shorter legs of ΔCED) being {{{96/7}}} and 4,
                      we get: {{{highlight_green(matrix(1,9, Area, of, triangle, CED, "(shaded)", "=", 1/2, "*", EC(ED)))}}} 
                                                                {{{matrix(1,4, "=", 1/2, "*", (96/7)4)}}}
                                                                {{{matrix(2,2, "=", (96/7)2, 
"=", 192/7)}}} 
                                                                {{{highlight_green(matrix(1,8, "=", 27&3/7, "=", "27.42857143,", or, 27.43, m^2, "(approximately)"))}}}</pre>