The diagonals of a parallelogram intersect at a 45 degree angle. If the diagonal lengths are 8 cm and 10 cm, what is the area of the parallelogram. Would appreciate an answer without trig.

Thanks

DungeyDabs Jul 12, 2019

#4**+3 **

Well.....if we can just use a "slight" bit of trig.....

The diagonals of a parallelogram bisect each other.....so.........these diagonals form four cogruent triangles

Each of these triangles will have two sides with lengths of 4 and 5 and an included angle between these sides of 45°

And the area of one of these triangles = (1/2) (product of these sides) * sine of the included angle

So.....the area of one of the triangles = (1/2) (4 * 5) * sin (45°)

[ sin (45° = √2 / 2 ]....so we have

(1/2) ( 4 * 5) ( √2/2)

(1/4) (20) * √2

And since we havefour of these triangles....the total area is

4 (1/4) * (20) * √2 =

20√2 units^2

CPhill Jul 12, 2019