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

AI Thread Summary
The discussion focuses on calculating the area of a parallelogram given its diagonals and one side length. Diagonal 1 measures 20 cm, diagonal 2 measures 37 cm, and side AB is 25.5 cm. Participants clarify that "S" represents the area and discuss using Heron's formula to find the area of triangle AMC formed by the diagonals. There is confusion about the relevance of the area of triangle AMC (306 cm) to the overall area of the parallelogram. Ultimately, it is emphasized that the provided measurements are sufficient to calculate the area without needing the triangle's area.
STS
Messages
5
Reaction score
0
diagonal 1=20cm.
diagonal 2=37cm.
AB=25.5cm

S (AMC)= 306cm.
S (ABCD)=?
 
Mathematics news on Phys.org
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?
 

Attachments

  • 333741DD-913B-4F0E-971E-5FF0F2D26C04.jpeg
    333741DD-913B-4F0E-971E-5FF0F2D26C04.jpeg
    11.5 KB · Views: 122
Last edited:
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...
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top