To find the area of a triangle with sides of length 12 cm, 6 cm, and 15 cm, you can use Heron's formula, which is a formula for finding the area of a triangle given the lengths of its sides. Heron's formula states that the area of a triangle with side lengths a, b, and c is:
A = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, defined as:
s = (a + b + c) / 2
In this case, the semi-perimeter of the triangle is:
s = (12 cm + 6 cm + 15 cm) / 2 = 21 cm
Plugging this value into Heron's formula gives:
A = √(21 cm(21 cm - 12 cm)(21 cm - 6 cm)(21 cm - 15 cm))
= √(21 cm(9 cm)(15 cm)(6 cm))
= √(21 cm * 135 cm^2)
= √(2835 cm^2)
= 53 cm
Therefore, the area of the triangle is approximately 53 cm^2.