MNOP is a parallelogram U is any point on side OP show that ar(MUN)=ar(PUM) + ar(UNO) - Maths - Areas of Parallelograms and Triangles

Question

MNOP is a parallelogram U is any point on side OP show that
ar(MUN)=ar(PUM) + ar(UNO)

Manbar Singh · Accepted Answer

We know that, when a ∆ and a ∥gm have common base and between same parallel lines, thenarea of ∆ = 12area of ∥gm
Now, ∆MUN and ∥gm MNOP have common base MN and between same parallel lines MN and OP , thenar∆MUN = 12ar ∥gmMNOP     
1⇒ar∥gmMNOP - ar∆PUM + ar∆UNO = 12area ∥gmMNOP⇒ar∆PUM + ar∆UNO = 12area of ∥gmMNOP     
2from 1 and 2, we getar∆MUN  = ar∆PUM + ar∆UNO

MNOP is a parallelogram.U is any point on side OP.show that ar(MUN)=ar(PUM) + ar(UNO)