SOLUTION: A rhombus has a perimeter of 80 meters and the length of one diagonal is 24 meters. Find the area of the rhombus.

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Question 187460This question is from textbook
: A rhombus has a perimeter of 80 meters and the length of one diagonal is 24 meters. Find the area of the rhombus.This question is from textbook

Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!


For the Area of a Rhombus, we take "half" of the product of the diagonals.
But we need to know the length of the sides which will be very helpful.
Knowing Perimeter we get--->P%5BR%5D=4%2AS
80m=4%2AS ---->cross%2880%2920%2Fcross%284%29=cross%284%29S%2Fcross%284%29
S=20m. *All Equal sides
Given one of the diagonal=24meters,
Let's see the illustration below:
drawing%28400%2C400%2C-1%2C6%2C-1%2C5%2Cline%280%2C0%2C1%2C3.5%29%2Cline%281%2C3.5%2C5%2C3.5%29%2Cline%285%2C3.5%2C4%2C0%29%2Cline%284%2C0%2C0%2C0%29%2Cgreen%28line%280%2C0%2C5%2C3.5%29%29%2Cgreen%28line%281%2C3.5%2C4%2C0%29%29%2Cred%28locate%282.2%2C1.7%2C90%5Eo%29%29%2Cred%28locate%282.4%2C2.2%2C90%5Eo%29%29%2Cred%28locate%282.7%2C2%2C90%5Eo%29%29%2Cred%28locate%282%2C2%2C90%5Eo%29%29%2Cblue%28locate%28-.2%2C0%2CA%29%29%2Cblue%28locate%28.8%2C3.5%2CB%29%29%2Cblue%28locate%285.2%2C3.5%2CC%29%29%2Cblue%28locate%283.5%2C0%2CD%29%29%2Cred%28locate%281.5%2C3%2C12m%29%29%2Cred%28locate%283%2C1%2C12m%29%29%2Cblue%28locate%283%2C3.8%2C20m%29%29%2Clocate%282.5%2C1.88%2CE%29%29
Given: BD=BE+ED=12+12=24meters; AC=AE+EC *note AE=EC

As you see we can get AE or EC by Pyth Theorem since it forms a Right Triangle:
20%5E2=BE%5E2%2BEC%5E2
EC%5E2=20%5E2-12%5E2=400-144=256
EC=sqrt%28256%29=red%2816meters%29=AE=EC
Therefore, Diagonal, +AC=AE%2BEC=16%2B16=red%2832meters%29

In conclusion, as we noted above, we take "half" of the product of the Diagonals: A=(1/2)(AC)(BD)=(1/2)(32m)(24m)=384sq.meter

Thank you,
Jojo