The area of a trapezium is  105cm2  and its height is  7cm . If one of the parallel sides is longer than the other by  6cm , the smaller side of trapezium is

The area of a trapezium is given by the formula:

Area = 1/2 * (sum of the lengths of the parallel sides) * height

We know that the area is 105 cm^2 and the height is 7 cm. We also know that one side is 6 cm longer than the other. Let's denote the shorter side as 'a' and the longer side as 'a + 6'.

Substituting these values into the formula, we get:

105 = 1/2 * (a + (a + 6)) * 7

Solving this equation will give us the length of the shorter side.

Step 1: Simplify the equation:

105 = 1/2 * (2a + 6) * 7

Step 2: Divide both sides by 7:

15 = 1/2 * (2a + 6)

Step 3: Multiply both sides by 2:

30 = 2a + 6

Step 4: Subtract 6 from both sides:

24 = 2a

Step 5: Divide both sides by 2 to solve for 'a':

a = 12

So, the shorter side of the trapezium is 12 cm.