The altitude of a triangle is 30 cm and its base is 80 cm. Find the area of the trapezoid formed by a line parallel to the base of the triangle and is 12 cm from the vertex.

Help please, I really have no idea. Can you show it with illustrations, thanks!

2. Hello, reiward!

The altitude of a triangle is 30 cm and its base is 80 cm.
Find the area of the trapezoid formed by a line
parallel to the base of the triangle and is 12 cm from the vertex.
Code:
                B
-             *
:            *| *
:           * |   *
:          *  |12   *
:         *   |       *
30      D *----+---------* E
:       *     |           *
:      *      |             *
:     *       |18             *
:    *        |                 *
- A *---------*-------------------* C
: - - - - - - 80- - - - - - - :
The area of a trapezoid is: .$\displaystyle A \;=\;\tfrac{h}{2}(b_1+b_2)$

. . where $\displaystyle h$ is the altitude and $\displaystyle b_1,b_2$ are the lengths of the parallel sides.

We already know: .$\displaystyle h = 18,\;b_1 = 80$
. . We need: .$\displaystyle b_2 \,=\,DE$

Since $\displaystyle \Delta DBE \sim \Delta ABC\!:\;\;\frac{DE}{12} \,=\,\frac{80}{30} \quad\Rightarrow\quad DE \,=\,32$

Therefore: .$\displaystyle A \;=\;\frac{18}{2}(80 + 32) \;=\;1008\text{ cm}^2$