Answer:
[tex]4x^{2}\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the rectangle minus the area of a kite
Step 1
Find the area of the rectangle
The area of the rectangle is equal to
[tex]A=bh[/tex]
In this problem we have
[tex]b=(3x+x)=4x\ units[/tex]
[tex]h=(x+x)=2x\ units[/tex]
substitute
[tex]A=(4x)(2x)=8x^{2}\ units^{2}[/tex]
Step 2
Find the area of a kite
The area of a kite is equal to
[tex]A=\frac{1}{2}D1D2[/tex]
where D1 and D2 are the diagonals of a kite
In this problem we have
[tex]D1=(3x+x)=4x\ units[/tex]
[tex]D2=(x+x)=2x\ units[/tex]
substitute
[tex]A=\frac{1}{2}(4x)(2x)=4x^{2}\ units^{2}[/tex]
Step 3
Find the area of the shaded region
[tex]8x^{2}\ units^{2}-4x^{2}\ units^{2}=4x^{2}\ units^{2}[/tex]
