What is the area of a quadrilateral ABCD, if AB = 5 cm, BC = 13 cm, CD = 9 cm, DA = 15 cm, AC = 12 cm?

6 answers

then you can use law of cosines to find a diagonal and you have two triangles.

(if you just have the 4 lengths and no angle, the shape is not uniquely determined.)
If you take the time to construct this quadrilateral and its diagonal, it can be seen that there are two triangles that each consist of a Pythagorean triad: 9, 12, 15 and 5,12, 13, meaning that both triangles are right angled.
Area of a right angled triangle is easy since the two short sides serve as the base and height. You can probably figure the rest out from here.
What is the area of quadrilateral ABCD, if AB = 5 cm, BC = 13 cm, CD = 9 cm, DA = 15 cm, AC = 12 cm?
rsm sucks
the area is 84
the answer is 84!!!