Question 704054: What is the area of the shaded region if
30cm 50cm
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1 1 ............1
20cm 1 ....1......................1
1 ........1..................... 1
1.--------1.................. 1 50cm
30cm 1 ........1............... 1
1 .....1............ 1
1 ...1......... 1
1________.1..____________________1
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I am guessing that your picture looks sort of like this:
 FJ and HE split rectangle ABCD into 4 smaller ones. BEFG is shaded.
(There are some squares, but a square is just a special kind of rectamgle).
I am not sure about the exact location of point G.
In your picture (as I see it), G is half way between H and B,
so I place my point G exactly half way,
but I'll make my explanation more general, so you can figure out any differences.
To calculate the area of BEFG in my drawing,
I would calculate the area of the large rectangle ABCD,
and then would subtract the areas of the unshaded triangles in the corners
(triangles AFG, DEF, and BCE).
You can use the same strategy for any similar problem,
and also if our drawings do not exactly match.
Those triangles at the corners are right triangles, and their area is east to calculate.
The area of triangle DEF is half of the area of rectangle DEIF,
so to calculate the area of DEF,
you just multiply the lengths of DE and DF, and then divide by 2.
It is the same way for all right triangles,
you multiply the length of the perpendicular sides and divide by 2.
For triangle DEF:
DE = 30cm, DF = 30cm, so
area of DEF = 
For triangle BCE:
BC = 50cm, EC = 50cm, so
area of DEF = 
For triangle AFG:
AF = 20cm,
In my drawing, I made HG=BG adding to HB = 50cm,
so HG=BG =  ,
and AG = AH + HG = 
With that length for AG,
area of AFG = 
For the large rectangle ABC:
side AB = AH + HB = 
side BC = 50cm
We multiply them to find the area:
area of ABCD = 
So, in my drawing
area of BEFG = area of ABCD - (area of DEF + area of BCE + area of AFG)
area of BEFG = 
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