Question

The sides of the trapezoid ABCD (BC//AD) are: AB=BC=CD=a and AD=2a.The line segment BE//CD, BE X AD = p.E. If the area of the triangle ABE= 5/2, then area of ABCD is:

Answer 1

see the diagram.

Draw perpendicular from B onto AD to meet AD at F.

ΔABE is isosceles, as BE = AB = CD = a
Using Pythagoras theorem,  BF = √3/2 a

Area of ΔABE = 1/2 * √3/2 a * (a/2 +a/2) = √3/4 a² = 5/2 units

Area of parallelogram ABCD = 1/2 * (AD+BC) * BF 
    = 1/2 * 3a * √3/2 * a = 3√3/4 * a² = 7.50 units