An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle

Sure, here are the steps to find the area of the isosceles triangle:

Step 1: Find the base of the triangle The perimeter of the triangle is the sum of all its sides. Since we know the perimeter is 30 cm and each of the two equal sides is 12 cm, we can find the base by subtracting the sum of the two equal sides from the perimeter.

So, Base = Perimeter - 2Side Base = 30 cm - 212 cm = 6 cm

Step 2: Find the height of the triangle In an isosceles triangle, a line drawn from the vertex angle (the angle between the two equal sides) to the base is the height and it bisects the base. This forms two right-angled triangles.

We can use the Pythagorean theorem (a^2 + b^2 = c^2) to find the height. Here, c is the length of the equal side (12 cm), b is half the base (6 cm / 2 = 3 cm), and a is the height we're trying to find.

So, a = sqrt(c^2 - b^2) Height = sqrt((12 cm)^2 - (3 cm)^2) = sqrt(144 cm^2 - 9 cm^2) = sqrt(135 cm^2) = 11.61 cm (approx)

Step 3: Find the area of the triangle The area of a triangle is given by the formula 1/2 * base * height.

So, Area = 1/2 * 6 cm * 11.61 cm = 34.83 cm^2 (approx)

So, the area of the isosceles triangle is approximately 34.83 cm^2.