Question

Calculate the area of trapezium CDEF.

Answer 1

We are given the two bases of the trapezium:

`ED = 5,\qquad AB = 9`

The formula for the area of the trapezium is

`A = ((B+b)h)/(2)`

So, we only need to figure out the length of the height EF.

We know that FA+EF = 11. Also, we're given that the perimeter of ABCF is 28, which means

`2AB+2FA = 28 \iff 2\cdot 9 + 2FA = 28 \iff 2FA = 10 \iff FA = 5`

So, we can deduce

`EF = 11-FA = 11-5=6`

And so we're ready to use the solving formula:

`A = ((5+9)\cdot 6)/(2) = (14\cdot 6)/(2) = 7\cdot 6 = 42`