Find the area of a rectangle of a triangle if its hypotenuse is 20 cm, and one of the legs is 12 cm.

Let’s find the second leg and the Pythagorean theorems: c² = a² + b².
b = √c² – a² = √400 – 144 = √256 = 16 cm.
Find the area of the triangle using Heron’s formula.
The length of the first side of the triangle: a = 12 cm.
The length of the second side of the triangle: b = 16 cm.
Length of the third side of the triangle: c = 20 cm.
Find the semiperimeter of a given triangle by the formula: p = (a + b + c) / 2 = (12 + 16 + 20) / 2 = 48/2 = 24.
We now calculate the area of a given triangle using Heron’s formula: S = √ (p * (p – a) * (p – b) * (p – c) = √24 * (24 – 12) * (24 – 16) * ( 24 – 20) = √24 * 12 * 8 * 4 = √9216 = 96 cm².
Answer: the area of a right-angled triangle is 96 cm².