Put the hypotenuse of two RT triangles and the right-angle side of the isosceles RT triangle together to form a right-angle trapezoid, and then:

S trapezoid = 2Sabc

S isosceles RT

(1)

b)(a)

b)/2=2*(ab/2)

c^2/2

(a^2

b^2)/2

ab=ab

c^2/2

a^2

b^2=c^2

2,

Using four congruent RT△, the right angles are spliced inward to form a diagonal A..

B, a

Quadrilateral of b

Then the spliced quadrilateral is a diamond.

S diamond =(a

b)(a)

b)/2

(The area of the diamond is half of the diagonal product)

Moreover, it can be proved that quadrilateral is square.

S squared = c 2

S diamond plaza

(1)

b)(a)

b)/2=c^2

Simplify:

a^2

b^2=c^2