+0  
 
0
65
2
avatar

ABCD is a rectangle of dimensions 2 and 4 as shown in the figure above.    

P and Q are points on the sides AB and CD, respectively, such that the straight line PQ is perpendicular to the diagonal DB and bisects it at point O.

Find the area of the quadrilateral CBOQ.

 

 Jan 14, 2021
 #1
avatar+1028 
+1

[CBOQ] = 2.75 square units

 Jan 15, 2021
 #2
avatar+116126 
+1

The area of the rectangle  = 4 * 2 =  8      (1)

 

And the area of triangle ABD is 1/2 of this =  4     (2)

 

O is the  center of the  rectangle =  (2,1)

 

The  slope of the line containing DB  = 2/4 = 1/2

 

So....the slope of the line containing QP   =   -2

 

And this line passes through  O,   so the equation of this line  is

 

y =   -2 ( x -2) + 1

 

y  = -2x  +  4 + 1

 

y= -2x + 5

 

We can find the x coordinate of Q  by  letting y = 0  

 

0  = -2x + 5

-5 = -2x

x = -5/-2 =  2.5

 

So the area   of triangle  DOQ =  (1/2) DQ * height =  (1/2) (2.5) (1) = 1.25  (3)

 

So....the area of the yellow region =   (1)  -(2) - (3)  = 

 

8  - 4  -  1.25   =

 

8  - 5.25  =

 

2.75  

 

cool cool cool

 Jan 15, 2021

90 Online Users

avatar
avatar
avatar
avatar