*Perimeter = x + x + y + 65 = 65 + 2x + y = 260*

* 2 x + y = 195 => x + (x+y) = 195 *

* x+y = 195 - x -------------------- equation 1*

* y - x = 195 - 3x ----------------- equation 2*

*Draw a perpendicular from the left end of 65.0 cm side , on to the side of y cm.*

*We get a square of size x by x and a right angle triangle, whose width is (y-x) and height is x.*

*Area of trapezoid = area of square + area of triangle *

* = x² + 1/2 x ( y - x ) = x² + 1/2 x y - 1/2 x²*

* = 1/2 x ( x + y ) substitute value of x+y from equation 1*

* = 1/2 x [195 - x ] = 97.5 x - 0.5 x²*

*IN the right side triangle,*

*x² + (y-x)² = 65²*

*x² + (195 - 3x)² = 65²*

*x² + 195² + 9x² - 2*3*195x = 65²*

*10 x² - 1170 x + 195² - 65² = 0 on simplification we get*

*x² - 117 x + 3380 = 0 *

*Δ = 117² - 4 * 3380 = 169*

*x = (117 + - 13 )/2 = 65 cm or 52 cm*

*Now y = 195 - 2x = 65 cm for x= 65 cm , or 91 cm for x = 52 cm*

*As it is said that y > x we choose the second set for x and y*

*Now area : ** 97.5 x - 0.5 x² = 97.5 * 52 - 0.5 * 52² = **3718 cm²*

**Please see Diagram.**