Find the area of a right-angled triangle if its leg and hypotenuse are 12 and 13, respectively.

We are given a right-angled triangle, and we also know that its leg and hypotenuse are 12 and 13, respectively.

In order to find the area of a right-angled triangle, we will use the formula:

S = 1/2 * a * b, where a and b are the legs of a right triangle.

By the Pythagorean theorem, we find the second leg of a right-angled triangle:

a ^ 2 + b ^ 2 = c ^ 2;

12 ^ 2 + x ^ 2 = 13 ^ 2;

x ^ 2 = 169 – 144;

x ^ 2 = 25;

x = 5.

So, 5 is equal to the length of the second leg.

Substitute in the formula and calculate the area of the triangle:

S = 1/2 * 5 * 12 = 60/2 = 30 sq. units.