One leg of a right triangle is 4in. long& and the hypotenus is 5in. long. What is the area of the triangle

You need base and height to determine area.
You have a right triangle; you can use the Pythagorean theorem to determine the length of the other leg.
a^2 + b^2 = c^2
4^2 + b^2 = 5^2
16 + b^2 = 25
b^2 = 9
b = 3

Area = (1/2)*base*height = (1/2)*3*4 = 6

Using the Pythagorean Theorem, if we let x denote the other leg, we see that the other leg is:
x^2 + 4^2 = 5^2 ==> x = 3.

Then, since the legs of the triangle denote the base and height of the triangle, the area is:
A = (1/2)bh
= (1/2)(3)(4)
= 6 in^2.

I hope this helps!

1/2 base * height
3,4,5 triangle
1/2 * 4 * 3 = 6" squared