1. **Stating the problem:** We are given a rectangle divided into areas A and B, and three triangular areas labeled 1, 2, and 3. We know that area 2 + area 3 equals half of the complete rectangle, which is also half of area A plus half of area B. We want to complete the formula and find the expression for area 2. 2. **Recall the formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ This formula applies to all triangles. 3. **Given:** $$\text{area 2} + \text{area 3} = \frac{1}{2} \times \text{area A} + \frac{1}{2} \times \text{area B}$$ 4. **Rewrite the equation:** $$\text{area 2} + \text{area 3} = \frac{1}{2} \text{area A} + \frac{1}{2} \text{area B}$$ 5. **Isolate area 2:** $$\text{area 2} = \frac{1}{2} \text{area A} + \frac{1}{2} \text{area B} - \text{area 3}$$ 6. **Since area 3 is also a triangle with base and height related to parts of the rectangle, and area 1 = area 2 + area 3 = half the rectangle, we can express area 2 as:** $$\text{area 2} = \frac{1}{2} (\text{base} \times \text{height})$$ where base and height correspond to the dimensions of the rectangle or its parts. 7. **Summary:** - area 2 + area 3 = 1/2 area A + 1/2 area B - area 2 = 1/2 (base × height) --- **Second question (not solved as per instructions):** How to quickly tell the number of faces, edges, and vertices of a triangular prism and a rectangular prism without counting every part.