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

In summary, the conversation discusses a parallelogram with diagonal lengths of 20cm and 37cm, and a side length of 25.5cm. The area of one of the resulting triangles (AMC) is given as 306cm. The question is how to calculate the area of the parallelogram (ABCD).
  • #1
STS
5
0
diagonal 1=20cm.
diagonal 2=37cm.
AB=25.5cm

S (AMC)= 306cm.
S (ABCD)=?
 
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  • #3
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?
 
  • #4

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  • #5
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.
 
  • #6
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...
 

1. What is a parallelogram?

A parallelogram is a four-sided shape with opposite sides that are parallel and equal in length. It also has opposite angles that are equal in measure.

2. How do you find the area of a parallelogram?

To find the area of a parallelogram, you can use the formula A = base x height, where the base is the length of one of the parallel sides and the height is the distance between the two parallel sides.

3. What are the diagonals of a parallelogram?

The diagonals of a parallelogram are the line segments that connect opposite corners of the shape. They bisect each other and divide the parallelogram into two congruent triangles.

4. How do you find the length of the diagonals in a parallelogram?

To find the length of the diagonals in a parallelogram, you can use the Pythagorean theorem. The length of the diagonal can be calculated by taking the square root of the sum of the squares of the lengths of the two adjacent sides.

5. Can you find the area of a parallelogram if you only know the length of the diagonals?

Yes, you can use the formula A = 1/2 x d1 x d2, where d1 and d2 are the lengths of the diagonals, to find the area of a parallelogram if you only know the length of the diagonals.

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