Question

Abcd and efgd are two parllelograms and g is the mid point of cd then prove that area of triangle dpc is equal to area of parallelogram efgd

Answer 1

Answer: Area of Δ DPC  =  area of Parallelogram EFGD

Step-by-step explanation:

D is mid point so, DG = GC

Δ DPG = Δ GPC - base for both is same and height is common as both lie in same parallel lines. ---- (1)

Area of Δ DPC = Area of  Δ DPG + Area of  Δ GPC = 2 Δ DPG  (based on 1)

Area of  Δ DPG = 1/2 Area of Δ DPC ----- (2)

Δ DPG and Parallelogram EFGD  lies in the same parallel lines and has same base.

So, area of Δ DPG  = 1/2 of area of Parallelogram EFGD --- (3)

Substitute (2) in (3)

1/2 Area of Δ DPC  = 1/2 of area of Parallelogram EFGD

So,

Area of Δ DPC  =  area of Parallelogram EFGD