1. ## Geometry Similarity

Can you please help me with this and show me where to go? Me and my family have no idea where to start

ABCD is a parallelogram. G is the midpoint of AD and F is the midpoint of AG. The area of the parallelograpm ABCD is 200cmsquared. Find the area of the quadrilateral BCGF

Thanks

Michael and family

2. Originally Posted by maltaman
Can you please help me with this and show me where to go? Me and my family have no idea where to start

ABCD is a parallelogram. G is the midpoint of AD and F is the midpoint of AG. The area of the parallelograpm ABCD is 200cmsquared. Find the area of the quadrilateral BCGF

Thanks

Michael and family
Call the length of side AD x and the length of AB y.

Then FG = x/4.

Now, the area of the parallelogram is given by
$A = xy~sin(\theta)$
where $\theta$ is the angle between AB and AD.

Now, BCGF is a trapezoid with bases BC and FG parallel. So it's area will be
$a = \frac{1}{2} \left ( x + \frac{x}{4} \right ) y~sin(\theta)$

Can you fill in the missing steps in my derivation and can you take it from here?

-Dan