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

Algebra ->  Surface-area -> SOLUTION: A rhombus has a perimeter of 80 meters and the length of one diagonal is 24 meters. Find the area of the rhombus.      Log On


   

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(1513) 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:

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