Let d be the diagonal and h the height of the isosceles trapezoid as shown in the fig above.
The base of isosceles triangle = (b – a)/2
We know the area of triangle = (1/2)base × altitude
(i) Perimeter = a + c + b + c = a + b + 2c
(ii) Area of an isosceles trapezoid (A) = Area of the rectangle + 2 × area of the triangle =
ah + 2 .
But h = 
(by applying
Pythagorean Theorem)
(by applying
Pythagorean Theorem)Substituting and simplifying we get
A = 
(iii) Diagonal length, d = 
(by applying
Pythagorean Theorem)
Substituting for h and simplifying we have
d = 