1. **State the problem:** We have an isosceles triangle with a base length of 24 cm and total area 220 cm². The triangle is divided into four smaller sections by three lines parallel to the base, dividing the equal sides into four equal segments. We need to find the area of the shaded third section from the top. 2. **Understand the division:** The three lines parallel to the base divide the triangle into four smaller trapezoids (or triangles at the top and bottom) with bases proportional to the segments on the equal sides. 3. **Key formula:** The area of a triangle is given by $$A = \frac{1}{2} \times \text{base} \times \text{height}$$. 4. **Important rule:** When lines are drawn parallel to the base in a triangle, the smaller triangles formed are similar to the original triangle. The lengths of their sides are proportional to the segments into which the equal sides are divided. 5. **Step to solve:** Calculate the height of the original triangle using the area formula. 6. **Step to solve:** Use similarity ratios to find the heights of the smaller triangles formed by the parallel lines. 7. **Step to solve:** Calculate the areas of the smaller triangles using the proportional heights and base lengths. 8. **Step to solve:** Subtract areas of smaller triangles to find the area of the shaded trapezoidal section. This approach uses similarity and proportionality to find the area of the shaded part without directly measuring it.