SOLUTION: Diagonal of a parallelogram is 30 meters long.The perpendiculars drawn on it from opposite vertices are 8m and 10 meters respectively.Find the area of the parallelogram

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Question 712379: Diagonal of a parallelogram is 30 meters long.The perpendiculars drawn on it from opposite vertices are 8m and 10 meters respectively.Find the area of the parallelogram
Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!
A quadrilateral is split into two triangles by a diagonal.
A segment perpendicular to the diagonal,
going from that diagonal to a vertex of the quadrilateral,
would be the altitude of one of those triangles.

We could find the area of that triangle knowing its
base (the length of the diagonal)
and its height (the length of the segment perpendicular to the diagonal, going to the vertex).
The quadrilateral of the problem is split by a 30-meter diagonal into two triangles.
Taking the 30-meter diagonal as base, the triangles' heights are 8 meters and 10 meters.
The area of the quadrilateral is the sum of the areas of the triangles, and can be calculated (in as

If you prefer to calculate the area of each triangle separately,
those areas are
and

The problem with the way you wrote the problem
is that your quadrilateral IS NOT A PARALLELOGRAM.
A parallelogram is split into two congruent triangles by each diagonal.
The parallel sides in a parallelogram have the same length,
so the triangles would have parallel sides with the same length,
and a shared side the diagonal.
That would make the two triangles congruent.
You could rotate one and superimpose it on the other.
The two triangles would have the same area and the same height.
Your triangles have different heights,
so your quadrilateral is not a parallelogram.