Answer:
[tex]6 units^2[/tex]
Step-by-step explanation:
The total area of the triangle is the area of the two smaller triangles added together.
We will use the equation of the area of the triangle as
[tex]A=\frac{1}{2}bh[/tex] - where b is the length of the base of the triangle, and h is the height of the triangle.
First, we can use the Pythagorean Theorem to find the base of the right hand side triangle.
The theorem states that:
[tex]a^2+b^2=c^2[/tex] - where c is the length of the hypotenuse, and a & b are the other side lengths.
[tex]2^2+b^2=3^2\\4+b^2=9\\b^2=5\\b=\sqrt{5}[/tex]
Now we can substitute in our values to determine the area of the right hand side triangle.
[tex]A=\frac{1}{2}*\sqrt{5} *2=\sqrt{5}[/tex]
As the two triangles have a shared base, we can now subtract our one base length to get the other base.
This gives us the base of our left hand side triangle as:
[tex]6-\sqrt{5}[/tex]
Now we can substitute this into our area equation, for the left hand side:
[tex]A=\frac{1}{2}*(6-\sqrt{5})*2=(6-\sqrt{5}) = (6-\sqrt{5})[/tex]
Now we add our two separate areas to get the overall area:
[tex]A=\sqrt{5}+6-\sqrt{5}=6[/tex]
