Answer:
A = 12
Step-by-step explanation:
Triangle AED is a right triangle because 3,4,5 is a pythagorean triple.
Angle EAD + Angle ADE = 90 (Because it is a right triangle)
and also:
Angle EAD + Angle BAE = 90 (Because it is one of the angles of the rectangle
Combining both you have:
Angle BAE = Angle ADE
Triangle ABE is similar to triangle ADE, therefore:
AE/AD = AB/ED = BE/AE
Using those relations you can calculate the width of the rectangle as follows:
AE/AD = AB/ED
3/5= AB/4
3*4/5= AB
2.4 = AB
Now the area is width * length:
A = 2.4*5=12.
Another way to do it is:
Draw a imaginary line from point E to segment AD lets call that new point Q, you get 2 rectangles:
ABEQ and EQDC
I hope you can appreciate that triangle ABE is half the area of rectangle ABEQ and triangle EDC is half the area of rectangle EQDC, then triangle AED is half the area of whole rectangle ABCD:
Area of ABCD = 2 * area of AED
= 2 * 3*4/2
= 12
