1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# In parallelogram ABCD. P is mid-point of AB. CP and BD intersect each other at point O. If area of ΔPOB=40cm2, find Area of Δ ABC and Parallelogram ABCD.

Open in App
Solution

## Area(ΔPOB)=40cm2Construct OE perpendicular to PB and OF perpendicular to CA.∴ area of ΔPOB=12OE×PB=40cm2Similarly,ar(DOC)=12OF×DC.ΔPE0∼ΔCFOOEOF=POCO=PECFΔPOB∼ΔDOC∴POCO=PBDC=12(since P is midpoint of AB)∴ar(POB)ar(DOC)=12OE×PB12OF×DC=OEOFPBDC=(POCO)2=14∴ar(DOC)=40×4=160cm2 Let ar(BOC)=y∴ar(ABC)=ar(BDC)=ar(BOC)+ar(DOC)=(y+160)cm2we know that area of two triangles between two parallel lines and same base are same.ar(PDC)=ar(BDC)ar(POD)+160=160yar(POD)=yar(APD)=ar(ABD)−ar(POD)−ar(POB)ar(APD)=160+y−y−40=120cm2ar(APD)=ar(PBC)=40+y∴40+y=120∴y=80cm2∴ar(BOC)=80cm2ar(ABC)=ar(BCD)=160+80=24080cm2ar(ABCD)=2ar(ABC)=480cm2

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Area of triangle
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program