The legs of the triangle are 3 cm and 4 cm, and the hypotenuse is 5 cm. Calculate the area of the triangle.

First way.

Since the triangle is rectangular, its area is half the product of the lengths of its legs.

S = a * b / 2 = 3 * 4/2 = 6 cm2.

Second way.

Let’s define the perimeter of the triangle:

P = 3 + 4 + 5 = 12 cm.

Let’s define the half-perimeter of the triangle: p = P / 2 = 12/2 = 6 cm.

We apply Heron’s theorem and determine the area of the triangle.

S = √p * (p – a) * (p – b) * (p – c).

S = √6 * (6 – 3) * (6 – 4) * (6 – 5) = √ (6 * 3 * 2 * 1) = √36 = 6 cm2.

Answer: The area of the triangle is 6 cm2.