Question

Question #6bc37

Answer 1

`A_2 = (A_1/2) (1 + (b / (a+b)))`

Explanation:

Area of a trapizoin `A = ((a+b) / 2) * h` where a, b are the parallel sides and h the distance between them.

`A_1 = ((a+b)/2) * h` Eqn (1)

Now base a has been halved or the new base is a/2
`A_2 = (((a/2) + b)/2) * h`

`A_2 = ((a+2b)/4)*h` Eqn (2)

Dividing Eqn(2) by (1),

`A_2 / A_1 = (((a+2b)/cancel4^2) * cancelh) / (((a+b)/cancel2) * cancelh)`

`A_2 = ((a + 2b) /(2* (a + b))) * A_1`

`A_2 = (A_1/2) (1 + (b / (a+b)))`