Given:
- Base of the isosceles triangle = 8 cm
- Perimeter of the triangle = 18 cm

To find:
- Area of the triangle

Solution:

Step 1: Finding the length of the equal sides
- An isosceles triangle has two equal sides.
- Let's assume the length of one of the equal sides is 'x' cm.
- Since the perimeter of the triangle is 18 cm, we can write the equation as:
Base + 2 * Equal sides = Perimeter
8 + 2x = 18
2x = 18 - 8
2x = 10
x = 10/2
x = 5

Step 2: Finding the area of the triangle
- The area of a triangle can be calculated using the formula:
Area = (Base * Height)/2

Step 3: Finding the height of the triangle
- In an isosceles triangle, the height is the perpendicular distance from the base to the vertex opposite the base.
- We can use the Pythagorean theorem to find the height.
- The height divides the isosceles triangle into two congruent right-angled triangles.
- Let's consider one of these right-angled triangles.
- The base of the right-angled triangle is half of the base of the isosceles triangle, which is 8/2 = 4 cm.
- The hypotenuse of the right-angled triangle is one of the equal sides of the isosceles triangle, which is 5 cm.
Using the Pythagorean theorem:
height^2 + base^2 = hypotenuse^2
height^2 + 4^2 = 5^2
height^2 + 16 = 25
height^2 = 25 - 16
height^2 = 9
height = sqrt(9)
height = 3

Step 4: Calculating the area
- Now that we have the base and height, we can substitute them into the area formula.
Area = (Base * Height)/2
Area = (8 * 3)/2
Area = 24/2
Area = 12 cm^2

Answer:
The area of the given isosceles triangle is 12 cm². Therefore, the correct option is A) 12 cm².