To find the area of the right triangle apply the formula: \(\displaystyle A=\frac{base\times height}{2}\)

Thus, the solution is: 

\(\displaystyle A=\frac{6\times 8}{2}=\frac{48}{2}=24\)

To find the area of this right triangle apply the formula: \(\displaystyle A=\frac{base \times height}{2}\)

Thus, the solution is:

\(\displaystyle A=\frac{12\times 6}{2}=\frac{72}{2}=36\)

In order to find the length of the longest side of the triangle (hypotenuse), apply the formula:

\(\displaystyle a^2 +b^2=c^2\), where \(\displaystyle a\) and \(\displaystyle b\) are equal to \(\displaystyle 6\) and \(\displaystyle 8\), respectively. And, \(\displaystyle c=\) the hypotenuse.

Thus, the solution is:

\(\displaystyle 6^2 +12^2=c^2\)
\(\displaystyle 36+144=c^2\)
\(\displaystyle 180=c^2\)
\(\displaystyle c=\sqrt{180}\)

To find the area of this triangle apply the formula: \(\displaystyle A=\frac{base\times height}{2}\)

Thus, the solution is:

\(\displaystyle A=\frac{13\times 8}{2}=\frac{104}{2}=52\)

This triangle only intersects with the vertical \(\displaystyle y\)-axis at one coordinate point: \(\displaystyle (0,-7)\). Keep in mind that the \(\displaystyle 0\) represents the \(\displaystyle x\) value of the coordinate and \(\displaystyle -7\) represents the \(\displaystyle y\) value of the coordinate point. 

The perimeter of this triangle can be found using the formula: \(\displaystyle P=height + base +\sqrt{height^2 +base^2}\)

Thus, the solution is:

\(\displaystyle P=13+8+\sqrt{8^2+13^2}\)
\(\displaystyle P=21 +\sqrt{64+169}\)
\(\displaystyle P=21+\sqrt{233}\)

In order to find the area of this triangle apply the formula: \(\displaystyle A=\frac{base \times height}{2}= \frac{4\times 3}{2}=\frac{12}{2}=6\)

In order to find the length of the longest side of the triangle (hypotenuse), apply the formula:

\(\displaystyle a^2 +b^2=c^2\), where \(\displaystyle a\) and \(\displaystyle b\) are equal to \(\displaystyle 13\) and \(\displaystyle 8\), respectively. And, \(\displaystyle c=\) the hypotenuse. 

Thus, the solution is:

\(\displaystyle 8^2+13^2=c^2\)
\(\displaystyle 64+169=c^2\)
\(\displaystyle c^2=233\)
\(\displaystyle c=\sqrt{233}\)

In order to find the length of the longest side of the triangle (hypotenuse), apply the formula:

\(\displaystyle a^2 +b^2=c^2\), where \(\displaystyle a\) and \(\displaystyle b\) are equal to \(\displaystyle 3\) and \(\displaystyle 4\), respectively. And, \(\displaystyle c=\) the hypotenuse. 

Thus, the solution is:

\(\displaystyle 3^2+4^2=c^2\)
\(\displaystyle 9+16=c^2\)
\(\displaystyle c^2=25\)
\(\displaystyle c=\sqrt{25}=5\)

The perimeter of this triangle can be found using the formula: \(\displaystyle P=height + base +\sqrt{height^2 +base^2}\)

Thus, the solution is:

\(\displaystyle P=3+4+\sqrt{3^2+4^2}\)
\(\displaystyle P=7+\sqrt{9+16}\)
\(\displaystyle P=7+\sqrt{25}\)
\(\displaystyle P=7+5=12\)