Parallelogram and triangle

Question

Could you please help me with this geometric task, as I cannot solve it by myself?

• Given: On the side CD of parallelogram ABCD is given point T, and point R is on the segment AT.

  Find :What percent of A(ABCD) is A(BTR) if:

  A) R is in the middle of AT

  B) AR : TR = 3 : 2 Thank you in advnace! I'd be grateful if you could help me.

Answer 1

By the formula of area of triangle and parallelogram we have:

A(ATB)=A(ABCD)/2

A(BTR)/A(ATB)=TR/TA

So A(BTR)/A(ABCD)=TR/(2TA)

So the answer for A) is 1/4 and the answer for B) is 1/5

Answer 2

Hint:

How the following triangles are related?

I hope this helps $\ddot\smile$