I think the second way is better
there are squares,so
1st way
JH=4
HF=2*4=8
from right triangle HFG
2*(HG)² =HF² by Pythagorean theorem
2*(HG)² =8² , (HG)² =32
also (HG)²=32 is the area of the small square
(JH/JC)²= A(small square)/A(large square)
(4/9)²=32/A(large square)
4²/9²=32/A
A(large square)=(9²*32)4² =81*32/16=162
162-32=130 cm² of the shaded area
2d way
from triangle JHG
4²+4²= 32 (side of small square)² ---Hypotenuse ², at the same time the area of the small square
from triangle JDC
9²+9²= 162(side of large square)² ---- hypotenuse² of the large triangle, at the same time the area of the large square
shaded area 162-32=130