Hello beq!xYou haven't told us much about the diagram, but I'll make the following assumptions:

- the sides of the base are a units long
- JK is parallel to AH
- M and N are the mid-points of the sides BG and AH

You need to know the formula:

- Area of a trapezium =

where the lengths of the parallel sides are and , and the height is .

So in BGKJ, the area we need is .

Now (I'm assuming!), and you can find LM using the Sine Rule on :

To find JK, you need to use the fact that triangles IJK and IAH are similar, together with the lengths of IL and IN. First IN: drop a perpendicular from I to the base, and then from the right-angled triangle thus formed:

From

So from similar triangles

Can you complete it from here?

Grandad