Question

The area of a trapezium is 315sqcm and the perpendicular distance between it's parallel sides is 20.4cm . What is the length of other side

Answer 1

Let the parallel lines be a and b

Given that difference of them is 6 cm

=> a - b = 6

Now we know that area of a trapezium =

\frac{1}{2} (a+ b)h \\

So, here given that area = 120 and

height = 8

=>

\frac{1}{2} (a + b) \times 8 = 120 \\ \\ = > (a + b) \times 4 = 120 \\ \\ = > (a + b) = \frac{120}{4} \\ \\ = > (a + b) = 30

So a + b = 30

But we are given that a - b = 6

Adding them,

a + b + a - b = 30 + 6

=> 2a = 36

=> a = 36/2

=> a = 18 cm

Now a + b = 30

=> 18 + b = 30

=> b = 30 - 18

=> b = 12cm

So first parallel side = 18 cm

another = 12 cm