The large triangle has the leg 7 meters and the hypotenuse 25 meters.


Hence, its other leg is   = 24 meters.


The area of the large triangle is   = 7*12 = 84 m^2.


The small triangle is similar to the large triangle with the similarity coefficient 4:7, or  
(from the smaller to the larger).


Hence, the area of the smaller triangle is   =  =  = 27  = 27.43  m^2  (rounded).    ANSWER

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 = (AB)(AC) = (7)(24) = 7(12) = 84 m2.
So, shorter leg (ED) of smaller ΔCED to shorter leg of larger ΔABC results in a   ratio. 
Thus, the area of smaller ΔCED will be: 
OR

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: 
7EC = 4(24) ---- Cross-multiplying 
. With lengths of EC and ED (longer and shorter legs of ΔCED) being  and 4,
                      we get: