1. **Problem statement:** We have an isosceles triangle with two equal sides of 5 cm and a base of 6 cm (divided into two segments of 3 cm each). A perpendicular height from the base midpoint to the apex is 4 cm. We want to find the surface area of this triangle. 2. **Formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Identify the base and height:** - Base $= 6$ cm (sum of two 3 cm segments) - Height $= 4$ cm (perpendicular segment from midpoint to apex) 4. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times 6 \times 4 = 3 \times 4 = 12$$ 5. **Interpretation:** The surface area of the isosceles triangle is $12$ square centimeters. This method uses the basic triangle area formula and the given dimensions directly.