1. **Stating the problem:** We have two large triangles sharing a common base of length 10 cm. The left triangle has height 7 cm, and the right triangle has height 12 cm. The total area of the non-shaded (unshaded) parts is 55 cm². We need to find the area of the shaded triangle formed near the base between the two large triangles. 2. **Formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Calculate the areas of the two large triangles:** - Left triangle area: $$A_1 = \frac{1}{2} \times 10 \times 7 = 35$$ - Right triangle area: $$A_2 = \frac{1}{2} \times 10 \times 12 = 60$$ 4. **Total area of both large triangles:** $$A_\text{total} = A_1 + A_2 = 35 + 60 = 95$$ 5. **Given the non-shaded area is 55 cm², the shaded area is the difference:** $$A_\text{shaded} = A_\text{total} - 55 = 95 - 55 = 40$$ 6. **Answer:** The area of the shaded triangle is **40 cm²**.