The area of a trapezium is 475 cm2 and the height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other

Let's denote the shorter parallel side of the trapezium as 'a' (in cm). According to the problem, the longer parallel side is 'a + 4' cm.

The formula for the area (A) of a trapezium is given by:

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

We can substitute the given values into this formula:

475 cm² = 1/2 * (a + a + 4) * 19 cm

Solving this equation will give us the lengths of the two parallel sides.

First, simplify the equation:

475 = 1/2 * (2a + 4) * 19

475 = (a + 2) * 19

Divide both sides by 19:

a + 2 = 475 / 19

a + 2 = 25

Subtract 2 from both sides to solve for 'a':

a = 25 - 2

a = 23 cm

So, the shorter parallel side (a) is 23 cm, and the longer parallel side (a + 4) is 23 + 4 = 27 cm.