We are given an isosceles triangle with two sides of length 5 cm and a base of length 8 cm. We need to calculate the area of this triangle.

1. Problem Description

We are given an isosceles triangle with two sides of length 5 cm and a base of length 8 cm. We need to calculate the area of this triangle.

2. Solution Steps

To find the area of the triangle, we need to find its height. Since the triangle is isosceles, the height from vertex A to the base BC bisects the base. Let h be the height. We can form a right triangle with hypotenuse 5 cm, one leg of length 4 cm (half of the base), and the other leg being the height h.

Using the Pythagorean theorem:

$a^2 + b^2 = c^2$

where a and b are the legs of the right triangle, and c is the hypotenuse.

In our case, $h^2 + 4^2 = 5^2$

$h^2 + 16 = 25$

$h^2 = 25 - 16$

$h^2 = 9$

$h = \sqrt{9}$

$h = 3$ cm

Now that we have the height, we can calculate the area of the triangle using the formula:

Area = $\frac{1}{2} \times \text{base} \times \text{height}$

Area = $\frac{1}{2} \times 8 \times 3$

Area = $\frac{1}{2} \times 24$

Area = $12$ cm$^2$

3. Final Answer

The area of the isosceles triangle is 12 cm$^2$.