Abcd is a trapezium with ab= x cm, dc=( x+ 4 )cm and the distance between the parallel sides ab and dc is 1/2 x cm
(a)- find and simplify, an expression in terms of x for the area of the trapezium.
the area of the trapezium is 84 cm2

(b)- calculate the value of x

We know that the smaller base is x cm, the greater base is x+4 cm, and that the height is x/2 cm.

Since the area of a trapezium is given by

If we plug the expressions we have

If this must equal 84, we can solve for x as follows: start with

Multiply both sides by 4:

Subtract 336 from both sides:

We can divide both sides by 2 to make computation simpler:

Use the quadratic formula (or any mean you prefer) to solve this equation and get the solutions

We can't accept the negative solution, because it would imply

and we can't have negative side lengths. So, the answer is 12.

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step-by-step explanation: