Answer:
[tex]\huge\boxed{A=3\dfrac{1}{3}}[/tex]
Step-by-step explanation:
Look at the picture.
Shadded region is a parallelogram.
The formula of an area of a prarallelogram:
[tex]A=bh\\\\b-base\\h-height[/tex]
We have the height h = 2.
Calculate the base.
Green triangles are congruent.
Use the Pytgagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have:
[tex]leg=x\\leg=2\\hypotenuse=3-x[/tex]
Substitute:
[tex]x^2+2^2=(3-x)^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\x^2+4=3^2-2(3)(x)+x^2\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\4=9-6x\qquad\text{subtract 9 from both sides}\\\\-5=-6x\qquad\text{divide both sides by (-6)}\\\\\dfrac{-5}{-6}=x\to x=\dfrac{5}{6}[/tex]
Therefore the base is:
[tex]b=3-x\to b=3-\dfrac{5}{6}=\dfrac{18}{6}-\dfrac{5}{6}=\dfrac{13}{6}[/tex]
Calculate the area:
[tex]A=\left(\dfrac{13}{6}\right)(2)=\dfrac{26}{6}=\dfrac{13}{3}=4\dfrac{1}{3}[/tex]
