Answer:
3600 square units
Step-by-step explanation:
From inspection of the given diagram, the area of the rectangle is:
[tex]\implies \sf Area=9 \cdot 4 = 36\; units \; squared[/tex]
Given matrix:
[tex]\left[\begin{array}{rr}5&10\\-8&4\end{array}\right][/tex]
To find the area scale factor, find the absolute value of the matrix determinant:
[tex]\implies \left| \:5 \cdot 4 - 10 \cdot (-8) \right|=\left|20+80\right|=100[/tex]
Therefore, the area of the image of the rectangle under the given matrix transformation is:
[tex]\implies \sf Area=36 \cdot 100=3600\;square\;units[/tex]
