We can use the Pythagorean theorem:
[tex]\sf a^2+b^2=c^2[/tex]
For right triangles, where 'a' and 'b' are the two legs and 'c' is the hypotenuse. Plug in what we know:
[tex]\sf 3.8^2+5^2=c^2[/tex]
Simplify the exponents:
[tex]\sf 14.44+25=c^2[/tex]
Add:
[tex]\sf 39.44=c^2[/tex]
Take the square root of both sides:
[tex]\sf c\approx \boxed{\sf 6.28~in}[/tex]
This is the length of the hypotenuse.
[tex]\sf A=\dfrac{1}{2}bh[/tex]
The base and the height are the two legs, plug them in:
[tex]\sf A=\dfrac{1}{2}(5)(3.8)[/tex]
Multiply:
[tex]\sf A=\boxed{\sf 9.50~in^2}[/tex]
The perimeter of any shape is the sum of all side lengths:
[tex]\sf 5+3.8+6.28=\boxed{\sf 15.08~in}[/tex]
