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

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    Area Parallelogram
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Discussion Overview

The discussion revolves around calculating the area of a parallelogram given the lengths of its diagonals and one side. Participants explore the relationship between the area of triangles formed by the diagonals and the area of the parallelogram itself, while also seeking clarification on certain notations used in the problem.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants provide the lengths of the diagonals (20 cm and 37 cm) and one side (25.5 cm) but express uncertainty about how to calculate the area of the parallelogram (S(ABCD)).
  • There is confusion regarding the notation "S( )" and the meaning of "M," with some participants questioning whether "M" refers to the midpoint of the diagonals.
  • One participant explains that S represents the area and describes a method involving moving one diagonal to form a triangle and using Heron's formula to find the area of that triangle (S(AMC)).
  • Another participant challenges the necessity of the area of triangle AMC (306 cm) for calculating the area of the parallelogram, suggesting that the provided information should suffice for the calculation.

Areas of Agreement / Disagreement

Participants express confusion and seek clarification on the notation and the relevance of certain values, indicating that there is no consensus on the approach to calculating the area of the parallelogram.

Contextual Notes

There are unresolved questions regarding the definitions of the terms used (e.g., "S( )" and "M") and the applicability of the area of triangle AMC in the context of finding the area of the parallelogram.

STS
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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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