The longer diagonal of a right trapezoid is 13 cm. the longer base is 12 cm. find the area of the trapezoid if the shorter base is 8 cm.

Draw a diagram of a right trapezoid . 
B C 
.| * 
.| * 
A D 
Longer diagnal BD = 13cm 
Longer base AD = 12cm 
Shorter base BC = 8cm 
Angle A is 90° , so △BAD is a right triangle . 
AB^2 + AD^2 = BD^2 
AB^2 + 12^2 = 13^2 
AB^2 + 144 = 169 
AB^2 = 25 
AB = 5 
So the area of trapezoid ABCD is (12+8)*5/2 = 50 [cm^2] .

Here are the answers to the ones that i could see.