Find the area of a right-angled triangle if the legs are 4 and 6 and the hypothesis is 8.

The condition says that we are given a right-angled triangle, and it is also known that the legs are 4 and 6, and the hypotenuse is 8. In order to find the area of a right-angled triangle, we will use the formula:

S = 1/2 * a * b;

The area of the triangle is half the product of the legs.

But we have also been given the hypotenuse. Let’s check if it is a right-angled triangle. Does the Pythagorean theorem hold.

a2 + b2 = c2;

16 + 36 = 64;

64 = 64.

The triangle is rectangular.

We are looking for the area of a triangle:

S = 1/2 * 4 * 6 = 12.

Answer: 12.