Consider a point A(m,n) , where m and n are positve intergers. B is the reflection of A in the line `y=x`, C is the reflaction of B in the y axis, D is the reflection of C in the x axis and E is the reflection of D is the y axis. The area of the pentagon ABCDE is.

Options

A. `2m (m+n)`
B. `m (m+3n)`
C. `m(2m+3n)`
D. `2m(m+3n)`

Answer

B

Explanation

Area of rectangle `BCDE=4mn`
Area of `DeltaABC=(2m(m-n))/(2)=m^2mn`
`therefore` Area of pentagon `ABCD=4mn+m^2-mn=m^2+3mn`