# ABCD is a trapezoid with line BC perpendicular to line AB and line BC perpendicular to line CD. AB=13 BC=12 CD=8.A line segment is drawn from A to E, which is the midpoint of line CD. What is the area of triangle AED?

Jan 6, 2016

${S}_{\triangle A E D} = 24$

#### Explanation:

The trapezoid described is somewhat as the figure below:

The formula of the area of the triangle is
${S}_{\triangle A E D} = \frac{b a s e \cdot h e i g h t}{2}$

Since AF is perpendicular to the triangle's side DE, and AF=BC=12, we have:
${S}_{\triangle A E D} = \frac{D E \cdot A F}{2} = \frac{4 \cdot 12}{2} = 24$