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