Question

In a parallelogram ABCD, P is a point in interior of parallelogram ABCD. If area of Parallelogram ABCD = 18cm.sq, then (area of triangle APD + area of triangle CPB ) is​

Answer 1

Answer:

EF∥AB⟶(1) [By construction]

∵AD∥BC

∵ opposite sides of a ∥gm are ∥al.

∴ AE∥BF⟶(2)

From equation (1) and (2), quadrilateral ABEF is a ∥gm. A quadrilateral is a ∥gm if its opposite sites are parallel. Similarly, quadrilateral CDEF is a ∥gm.

∵△APB and ∥gm ABFE are on the same base AB and between the same ∥als AB and EF.

∴ar(△APB)=

2

1

ar(∥gmABFE)⟶(3)

∵△PCD and ∥gm CDEF are on the same base DC nd between the same ∥als DC and EF.

∴ar(△PCD)=

2

1

ar(∥gmCDEF)⟶(4)

Adding equations (3) and (4), we get

ar(△APB)+ar(△PCD)=

2

1

[ar∥gmABEF+∥gmCDEF]

=

2

1

ar∥gmABCD

=

2

1

×8 =9cm

2