The lengths of the parallel sides of a trapezium are 9cm and 12cm. If the area of the trapezium is 105cm\(^{2}\), find the perpendicular distance between th...

To find the perpendicular distance between the parallel sides of a trapezium, we can use the formula for the area of a trapezium. The formula for the area of a trapezium is given by: Area = (1/2) * (sum of parallel sides) * (perpendicular distance between the parallel sides) In this case, we are given: Length of one parallel side = 9 cm Length of the other parallel side = 12 cm Area of the trapezium = 105 cm² Let's denote the perpendicular distance between the parallel sides as "h." Using the formula for the area of a trapezium, we can rewrite it as: 105 = (1/2) * (9 + 12) * h Simplifying the equation: 105 = (1/2) * 21 * h Multiplying both sides by 2 to eliminate the fraction: 210 = 21h Dividing both sides by 21 to solve for "h": h = 210 / 21 h = 10 cm Therefore, the perpendicular distance between the parallel sides of the trapezium is 10 cm. So, the correct answer is 10 cm.