If the area of the trapezium whose parallel sides are 6 cm and 10 cm is 32 sq. cm, then the distance between the parallel sides is

### Concept & Formula To find the height when the area and parallel sides are given, rearrange the standard area formula for a trapezium. $$Area = \frac{1}{2} \times (Sum\ of\ parallel\ sides) \times height$$ $$h = \frac{2 \times Area}{a + b}$$ ### Step-by-Step Solution * **Given:** Area = $32\text{ cm}^2$, side $a = 6\text{ cm}$, side $b = 10\text{ cm}$. * **Substitute into Formula:** $32 = \frac{1}{2} \times (6 + 10) \times h$ * **Solve for $h$:** $32 = \frac{1}{2} \times 16 \times h$ $32 = 8 \times h$ $h = \frac{32}{8} = 4\text{ cm}$. ### Exam Strategy & Shortcut Find the average of the parallel sides: $(6 + 10) / 2 = 8$. The area is this average multiplied by the height. So, $8 \times h = 32$, which immediately gives $h = 4$. ### Common Pitfall Adding the parallel sides but forgetting to divide by 2, setting up the equation as $32 = 16 \times h$, which leads to the incorrect answer of 2. ### Final Answer Therefore, the correct answer is **4 cm**.