SOLUTION: Diagonals AC and BD of a parallelogram ABCD intersect at O . Given that AB=12 gm and the perpendicular distance between AB and DC is 6 cm. Calculate the area of the triangle AOD

Algebra ->  Pythagorean-theorem -> SOLUTION: Diagonals AC and BD of a parallelogram ABCD intersect at O . Given that AB=12 gm and the perpendicular distance between AB and DC is 6 cm. Calculate the area of the triangle AOD       Log On


   

Question 1034407: Diagonals AC and BD of a parallelogram ABCD intersect at O . Given that AB=12 gm and the perpendicular distance between AB and DC is 6 cm. Calculate the area of the triangle AOD
Answer by ikleyn(52779) About Me  (Show Source):
You can put this solution on YOUR website!
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The area of the triangle AOD is one fourth of the area of the parallelogram, which is 12*6 = 72 cm%5E2.

So the answer is 72%2F4 = 18 cm%5E2.

Why? Due to two reasons.

1. Because the diagonal of a parallelogram divides it in two congruent triangles, and

2. Because the diagonals of a parallelogram bisect each other.


See the lessons
      - In a parallelogram, each diagonal divides it in two congruent triangles
      - Properties of diagonals of parallelograms
in this site.