Posted by **Sanjna** on Friday, September 30, 2011 at 4:44am.

In parallelogram ABCD, P is mid-point of AB.CP and BD intersect each other at point O. If area of triangle POB = 40 cm^2,

find : (i) OP :OC

(ii) areas of triangle BOC and PBC

(iii) areas of /\ ABC and parallelogram ABCD ? ?

- Geometry -
**Reiny**, Friday, September 30, 2011 at 9:37am
Did you make your sketch?

Notice that ∆PBO is similar to ∆CDO

let PB = 1, then CD = 2 (remember AB was bisected)

then OP : OC = 1 : 2

let's fill in areas:

∆POB = 40 (given)

∆PBO = 40 , (same base, same height)

∆COD = 160 ( areas proportional to square of sides)

let ∆BCO = x

let ∆AOD = y

x + 160 = y + 80

y = x+80

now look at ∆PBC and ABD , they have the same height, but bases of 1 and 2

so x+40 = (1/2)(y+80)

2x + 80 = y+80

2x = y , ahhhh!

then 2x = x+80

x = 80 and y = 160

Now we know it all, take it from here.

## Answer This Question

## Related Questions

- geometry - Open that link please please help me with my assignments 1. in the ...
- GEOMETRY URGENT PLEASE - (imageshack)(.)us(/)photo (/) my-images (/)42(/)2vja. ...
- geometry PLEASE - imageshack(.)(us)/photo/my-images/42/2vja.jpg/ Open that link ...
- GEOMETRY - Here are the figures. file:///C:/Users/ALIZAJOY/Pictures/Untitled....
- Geometry - D is the mid-point of side AB of the triangle ABC, E is mid-point of ...
- geometry - (imageshack)123 (.)us(/)photo 123 (/) my-images 123 (/)42(/) 123 ...
- Geometry - Diagonals of quadrilateral ABCD intersect at O.If area of triangle ...
- math - Triangle ADE is inside rectangle ABCD. Point E is half way between points...
- Geometry - I have four questions: 1. The area of trapezoid ABCD is 60. One base ...
- maths-areas - in triangle ABC P, Q AND R ARE the mid points of side AB, BC, CA....

More Related Questions