SOLUTION: the figure shows ABCD as a trapezium in which AB=(5x+6) cm, DC= 3x cm and the height between the parallel line is (4x-3) cm. Show that the area of the trapezium can be expressed as

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: the figure shows ABCD as a trapezium in which AB=(5x+6) cm, DC= 3x cm and the height between the parallel line is (4x-3) cm. Show that the area of the trapezium can be expressed as      Log On


   

Question 627536: the figure shows ABCD as a trapezium in which AB=(5x+6) cm, DC= 3x cm and the height between the parallel line is (4x-3) cm. Show that the area of the trapezium can be expressed as (16x^2 - 9) cm2
Found 2 solutions by math175, ikleyn:
Answer by math175(1) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer by ikleyn(52848) About Me  (Show Source):
You can put this solution on YOUR website!
.
the figure shows ABCD as a trapezium in which AB=(5x+6) cm, DC= 3x cm and the height between the parallel line is (4x-3) cm.
Show that the area of the trapezium can be expressed as (16x^2 - 9) cm2
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The area of a trapezoid (of any trapezoid) is the product of the half sum of the base lengths by the altitude.


In your case the half sum of the base lengths is 

%281%2F2%29%2A%28abs%28AB%29%2Babs%28DC%29%29 = %281%2F2%29%2A%28%285x%2B6%29+%2B3x%29 = %281%2F2%29%2A%288x%2B6%29 = 4x%2B3.

Therefore, the area of your trapezoid is

%284x%2B3%29%2A%284x-3%29 = 16x%5E2-9.

It is what has to be proved.

Solved.


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