A rectangle and a parallelogram have equal areas. If the sides of the rectangle are 10 m and 12 m and the base of the parallelogram is 20 m, then the altitude of the parallelogram is

### Concept & Logic Equate the area formulas of the two distinct geometric shapes given that they share the exact same area value. $$\text{Area of Rectangle} = \text{Length} \times \text{Width}$$ $$\text{Area of Parallelogram} = \text{Base} \times \text{Altitude}$$ ### Step-by-Step Solution 1. **Calculate the Area of the Rectangle:** * Area = $10 \text{ m} \times 12 \text{ m} = 120 \text{ m}^2$ 2. **Set up the Parallelogram equation:** * Since the areas are equal, the Parallelogram's area is also $120 \text{ m}^2$. * Base = 20 m * Area = Base $\times$ Altitude * $120 = 20 \times \text{Altitude}$ 3. **Solve for Altitude:** * Altitude = $120 / 20 = 6 \text{ m}$ ### Exam Strategy & Shortcut Write it as a single line equation: $10 \times 12 = 20 \times h$. Cancel out a 10 from both sides: $12 = 2 \times h$, leading immediately to $h = 6$. ### Common Pitfall Misreading "altitude" as a slant edge and attempting to use the Pythagorean theorem unnecessarily. Altitude simply means the perpendicular height. ### Final Answer Therefore, the correct answer is **6 m**.