Find the area of a triangle two side of the triangle are 18 cm, and 12 cm. and the perimeter is 40 cm.

To find the area of a triangle using two sides and the perimeter, we first need to find the length of the third side.

Step 1: Find the third side The perimeter of a triangle is the sum of the lengths of all its sides. Given that the perimeter is 40 cm and two sides are 18 cm and 12 cm, we can find the third side as follows:

Third side = Perimeter - Sum of two given sides Third side = 40 cm - (18 cm + 12 cm) Third side = 40 cm - 30 cm Third side = 10 cm

Step 2: Find the semi-perimeter The semi-perimeter of a triangle is half its perimeter. We can find the semi-perimeter as follows:

Semi-perimeter = Perimeter / 2 Semi-perimeter = 40 cm / 2 Semi-perimeter = 20 cm

Step 3: Find the area We can find the area of the triangle using Heron's formula, which is given as follows:

Area = sqrt[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter and a, b, and c are the sides of the triangle. Substituting the given values, we get:

Area = sqrt[20(20 - 18)(20 - 12)(20 - 10)] Area = sqrt[2028*10] Area = sqrt[3200] Area = 56.57 cm^2

So, the area of the triangle is approximately 56.57 cm^2.