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

From the properties of a right-angled triangle, it is known that its area is equal to half the product of its two legs and is found by the formula:
S = (a * b) / 2, where S is the area of ​​a right-angled triangle, a and b are legs.
We only know one leg. Find the second leg, knowing the length of the first leg and the length of the hypotenuse, using the Pythagorean theorem:
b = √ (c ^ 2 – a ^ 2), where c is the hypotenuse.
Substitute the known values ​​into the expression, solve the resulting equation and find the length of the second leg:
b = √ (13 ^ 2 – 12 ^ 2) = √ (169 – 144) = √25 = 5 (conventional units).
Knowing the length of the two legs of a right-angled triangle, we find its area:
S = (12 * 5) / 2 = 60/2 = 30 (conventional square units).
Answer: S = 30 conventional square units.