Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.

Here, the sides of triangle are a = 18 cm, b = 10 cm and primeter is 42 cm.
We Know that the parimeter of triangle = a + b + c
⇒ 42 = 18 + 10 + c
⇒ c = 14 cm
So, the semi- perimeter of triangle is given by
S = a + b + c/2 = 42/2 = 21 cm
Therefore, using Heron’s formula, the area of triangle = √s(s – a)(s – b)(s – c)
= √21(21 – 18)(21 – 10)(21 – 14)
= √21(3)(11)(7)
= √7 × 3 × (3)(11)(7)
= 7 × 3√11 = 21√11 cm²
Hence, the area of triangle is 21√11 cm².