In a right-angled triangle ABC, angle C = 90 degrees, AB = 10cm, inscribed circle radius = 2cm.

In a right-angled triangle ABC, angle C = 90 degrees, AB = 10cm, inscribed circle radius = 2cm. Find the area of this triangle.

We use the formula for the radius of the inscribed circle for a right-angled triangle through the lengths of its sides and determine the sum of the lengths of the legs (BC + AC)

R = OH = (AC + BC – AB) / 2.

(AC + BC – AB) = 2 * R

(BC + AC) = 2 * R + AB = 2 * 2 + 10 = 14 cm.

Let’s define the semiperimeter of the triangle ABC. p = (AB + AC + BC) / 2 = 24/2 = 12 cm.

Through the formula for the radius of the inscribed circle, we determine the area of the triangle ABC.

R = S / p.

S = R * p = 2 * 12 = 24 cm2.

Answer: The area of the triangle ABC is 24 cm2.