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In the figure ABCD is a 3 cm sided square, GC = FC = 1 cm, find the area of EFGC in square centimeter.

 

 May 22, 2020
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Let D  =  (0,0)

Let C = (3,0)

Let G  = (2,0)

Let  F= ( 3,1)

Let B  =  (3,3)

 

The slope  of DF  =  [ 1 - 0] /  [ 3 - 0 ]  =  1/3

So   the equation of  the  line  containing  DF  =  (1/3)x

 

The slope  of BG   =  [ 3-0]  / [3 - 2]  =  3/1  =  3

So  the equation of  the line containing BG  =  3(x - 3)  +  3   =   3x - 6

 

We can find  the x coordinate of the intersection of  these lines can be found as

 

(1/3)x  =  3x - 6     rearrange  as

 

6  =  [ 3 - 1/3]x

6  = (8/3]  x

x  = (3 * 6 / 8]  =  18/8   =  9/4  =  x coordinate of E

 

The  y coordinate of E  =   (1/3)(9/4)  =  9/12   =  3/4  =  height of  triangle DGE

 

Area  of triangle  DGE  = (1/2)DG * height  =  (1/2) (2) * (3/4)  =  3/4

 

Area of triangle DFC = (1/2) DC * CF  = (1/2)(3) (1)  =  3/2

 

Area  of EFGC  =   area of triangle DFC  - area of triangle DGE =  (3/2)  - (3/4)  =  (3/4)cm^2  = .75 cm^2

 

 

cool cool cool

 May 22, 2020

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