If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio of the area of the triangle to the area of the parallelogram is __________.
 

It is known that, if a parallelogram and a triangle are on the same base and between the same parallels, then the area of the triangle is half the area of the parallelogram. 

Proof:

Here, $∆$ABD and parallelogram ABCD are on same base AB and between same parallels AB and DC.

We know area of triangle = $\frac{1}{2}\times$base $\times$ height

In  $∆$ABD, base = AB and height = DE

Therefore, area ($∆$ABD) = $\frac{1}{2}\times$AB $\times$ DE    .............(1)

We know, area of parallelogram = base $\times$height

In parallelogram ABCD, base = AB and height = DE

Therefore, area (ABCD) = AB $\times$ DE               .............(2)

Therefore, from equation (1) and (2), we get:

area ($∆$ABD) = $\frac{1}{2}\times$area (ABCD)

area ($∆$ABD) :  area (ABCD)  = 1: 2

 ∴ The ratio of the Area of the triangle to the Area of the parallelogram = 1: 2