Solving for the area of a triangle in a quadrilateral

Hi Guys,

I've never been good with geometry, and this one just has me stumped. I cannot find any ratios to help me solve the problem.

I will use [ ] to denote area.

We have quadrilateral ABCD, and the point E which is the intersection of the diagonals of ABCD. [AEB] = 3, [DEC] = 10, [BEC] = 2 *[AED]

Compute [AED].

Re: Solving for the area of a triangle in a quadrilateral

Hey ShadowKnight8702.

In your quadrilateral you have [ABCD] = [AEB] + [DEC] + [BEC] + [AED] = [AEB] + [DEC] + 2*[AED] (using the definition that the whole quadrilateral is the sum of each of the quarters separated from the mid-point E and the appropriate lines.

1 Attachment(s)

Re: Solving for the area of a triangle in a quadrilateral

Hi,

The answer is $\displaystyle \sqrt{15}$. The attachment shows how to arrive at this. I had fun constructing an accurate drawing of the situation.

Attachment 29043

Re: Solving for the area of a triangle in a quadrilateral