<prompt> Find the area of a triangle with sides of 12 cm, 15 cm, and 18 cm.  <response>: A triangle with sides of 12 cm, 15 cm, and 18 cm is a right-angled triangle. This can be proven using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse the longest side is equal to the sum of the squares of the other two sides. So, in this case, 182 122 152, or 324 144 225.The area of a right-angled triangle can be calculated as half the product of the lengths of two sides forming the right angle. So, the area of this triangle is 12 cm 15 cm2 90 cm2. In other words, the triangle has an area of 90 square centimeters. 