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

In parallelogram ABCD. P is the mid-point of AB. CP and BD intersect each other at point O. If area of ΔPOB=40cm2. Find the area of ΔBOC.

Open in App
Solution

We know that the ratio of the areas of the two similar triangles is equal to the square of the ratio of the corresponding sides therefore,

Ar(ΔPOB)Ar(ΔCOD)=(POCO)2

Ar(ΔCOD)=40×4=160cm2
Let the area of triangle BOC be 'y'.

We know that area of two triangles between the two parallel lines are equal so,

Ar(ΔPDC)=Ar(ΔBDC)

Ar(ΔPOD)+160=160+y

Ar(ΔPOD)=y

Similarly,

Ar(ΔADP)=Ar(ΔBCP)

Ar(ΔADP)=40+y

Now,

2Ar(ΔBCD)=Ar(ABCD)

2(160+y)=(160+y)+(40+y)(40+y)

320+2y=240+3y

3y2y=320240

y=80

Therefore,

Ar(ΔBOC)=80cm2

Ar(ΔPBC)=120cm2


407368_196353_ans.jpg

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Parallelograms
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon