Given the area of a square = 100mm square
Also the area of a rhombus = 80mm square
![\begin{gathered} Areaofsquare=100\operatorname{mm} \\ \text{length of the side =l} \\ A=l^2 \\ 100=l^2 \\ l=\sqrt[]{100}=10\operatorname{mm} \end{gathered}]()
![\begin{gathered} Areaofrhombus=80\operatorname{mm} \\ so\text{ the altitude =}(80)/(10)=8\operatorname{mm} \\ GF=\sqrt[]{10^2-8^2} \\ GF=\sqrt[]{36}=6\operatorname{mm} \end{gathered}]()
![\begin{gathered} Areaoftriangle\text{ GFD=}(1)/(2)bh \\ =(1)/(2)*6*8=(48)/(2)=24\operatorname{mm} \end{gathered}]()
To solve for the area of the shaded region , you will calcuate the area of the triangle out of the two shape, then subtract the area of the triangle from the rhombus and also from the square.
![\begin{gathered} Areaofshadedregion\text{ = }100-(80-24) \\ =100-56 \\ =44\operatorname{mm} \end{gathered}]()
Hence the area of the Shaded region = 44mm square