SOLUTION: Two Parallel sides DC & AB of a trapezium are 12 cm and 36 cm respectively. If non parallel sides are 15 cm each.Find the area of the trapezium?

Algebra ->  Surface-area -> SOLUTION: Two Parallel sides DC & AB of a trapezium are 12 cm and 36 cm respectively. If non parallel sides are 15 cm each.Find the area of the trapezium?      Log On


   

Question 574813: Two Parallel sides DC & AB of a trapezium are 12 cm and 36 cm respectively. If non parallel sides are 15 cm each.Find the area of the trapezium?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The trapezoid (the US word for the UK word "trapezium") 
is isosceles:

 

We will draw altitudes AF and BE  (in green) perpendicuilar to DC.  Since
EF = AB = 12cm, and 12cm is 1%2F3 of DC which is 36cm, DF amd EC are also
12cm each.

 

We can find altitude AF by applying the Pythagorean theorem to right 
triangle ADF:

                    AF² + DF² = AD²
                    AF² + 12² = 15²
                    AF² + 144 = 225
                          AF² = 81
                           AF = 9cm

 


          Area =(Average of parallel sides)·(altitude)

          Area = %28AB%2BDC%29%2F2·AF

          Area = %2812cm%2B36cm%29%2F2·9cm
          
          Area = 48cm%2F2·9cm
            
          Area = 24cm·9cm

          Area = 216cm²

Edwin