# Area of Quadrilateral given diagonals and 1 side.

• Oct 17th 2009, 11:52 PM
itsmaximhere
Area of Quadrilateral given diagonals and 1 side.
Can some one help me out please...

In a quadrilateral ABCD, the diagonals AC and BD intersect at O. Let OA = 2, OB = 2, OC = 3, OD = 4 and AB = 3. The area of the quadrilateral is ?

Im sorry if this is too simple....
• Oct 18th 2009, 02:12 AM
aidan
Quote:

Originally Posted by itsmaximhere
Can some one help me out please...

In a quadrilateral ABCD, the diagonals AC and BD intersect at O. Let OA = 2, OB = 2, OC = 3, OD = 4 and AB = 3. The area of the quadrilateral is ?

Im sorry if this is too simple....

The area (K) of a quadrilateral can be found by

$K = \dfrac{1}{2} pq \sin \theta$

the diagonals are p & q

In this case, from the data give:
p = 2+3 = 5 & q = 4+2 = 6

You have given the three sides of a triangle: 2,2,3
Use the cosine law to compute $\angle AOB = \theta$

Probably easier (since $\triangle AOB$ is isosceles)
$\theta = 2 \, sin^{-1} \left ( \dfrac{1.5}{2} \right)$

Compute $\theta$ and $\sin \theta$, then plug them into the equation above.