Parallelogram with diagonals. Need to find the area (S).

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SUMMARY

The discussion centers on calculating the area of a parallelogram using its diagonals and one side length. Given diagonal lengths of 20 cm and 37 cm, along with a side length of 25.5 cm, the area of the parallelogram (S) can be derived using Heron's formula. The area of triangle AMC is noted as 306 cm², but this value is not necessary for calculating the area of the parallelogram itself. The key takeaway is that the area can be computed directly from the provided dimensions without needing to reference the area of triangle AMC.

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diagonal 1=20cm.
diagonal 2=37cm.
AB=25.5cm

S (AMC)= 306cm.
S (ABCD)=?
 
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STS said:
diagonal 1=20cm.
diagonal 2=37cm.
AB=25.5cm
Okay, that makes sense.

S (AMC)= 306cm.
S (ABCD)=?
What?? What is "S( )"? What is "M"? Is it another point? The midpoint where the two diagonals intercept?
 

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Country Boy said:
Okay, that makes sense.What?? What is "S( )"? What is "M"? Is it another point? The midpoint where the two diagonals intercept?

S is the area. You move one of the diaganals to the side, then that forms a triangle. Then with Heron's formula you figure out the area of the triangle that has formed (AMC). That is suppose to help you figure out the area of the parallelogram using another formula, but I couldn't figure it out.
 
STS said:
S is the area. You move one of the diaganals to the side, then that forms a triangle. Then with Heron's formula you figure out the area of the triangle that has formed (AMC). That is suppose to help you figure out the area of the parallelogram using another formula, but I couldn't figure it out.
OK; then WHY did you post only this:
........
diagonal 1=20cm.
diagonal 2=37cm.
AB=25.5cm

S (AMC)= 306cm.
S (ABCD)=?
........

You're given the 2 diagonals plus 1 side.
That's plenty of info to calculate the area.
S(AMC) = 306 not required...
 

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