That diagonal will split the rectangle into two triangles, with 5 inches being the hypotenuse of each. If we know that one base is 4 inches, then we can use the Pythagorean theorem to find the length of the other side of the rectangle. Let's call that other side x for now. x^2+4^2=5^2, because of the pythagorean theorum.
[tex] x^{2} +4^{2} = 5^{2} [/tex]
[tex] x^{2} +16=25[/tex]
[tex] x^{2} =9[/tex]
[tex]x=3[/tex]
So 3 is the other side of the rectangle, take that times 4 and you'll get 12 in^2.
