Find the area of the shaded region

eddy2017

eddy2017

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Hi, this problem should be easy for me at this stage of the game but i'm posting it because i want to make sure i follow the right procedures
I am attaching a pic20220205_144614.jpg
 
my work
[math]I found the area of the non-shaded region first[/math][math]A=l*w[/math][math]A=9in*10in[/math][math]A=90in^2[/math]
[math]shaded region[/math][math]A=l*w[/math][math]A=11in*14in[/math][math]A=154in^2[/math]
now, to find the area of the shaded region, I subtract the area of the non shaded area from it
[math]154in^2-90in^2[/math][math]Area of shaded region 64 in^2[/math]
Is this correct?
thanks
 
Yes, correct method and answer.

(A little note - you have used 'shaded region' in referring to the large rectangle and in referring to the actual shaded region).
 
eddy2017 said:
my work
[math]I found the area of the non-shaded region first[/math][math]A=l*w[/math][math]A=9in*10in[/math][math]A=90in^2[/math]
[math]shaded region[/math][math]A=l*w[/math][math]A=11in*14in[/math][math]A=154in^2[/math]
now, to find the area of the shaded region, I subtract the area of the non shaded area from it
[math]154in^2-90in^2[/math][math]Area of shaded region 64 in^2[/math]
Is this correct?
thanks
Click to expand...
Your work would be some what correct - if those regions were rectangles. Nowhere in the image I could find that statement (assertion).

and the second group of calculation starts with the following statement:

[math]shaded region[/math] ................... really - I don't think so. Later you said

[math]Area of shaded region 64 in^2[/math] ............... this is however is correct. You need to read/write carefully and review your statements.
 
lex said:
Yes, correct method and answer.

(A little note - you have used 'shaded region' in referring to the large rectangle and in referring to the actual shaded region).
Click to expand...
I'm confused here. Isn't the shaded region that of the whole rectangle except for the area that occupies the white area (non-shaded)?
 
Subhotosh Khan said:
Your work would be some what correct - if those regions were rectangles. Nowhere in the image I could find that statement (assertion).
Click to expand...
but these are rectangles, aren't they?. they are not squares!

A rectangle is a 2D shape that has 4 sides, 4 corners, and 4 right angles. Opposite sides of a rectangle shape are the same length, with one pair being longer than the other pair. If all the sides of a rectangle were the same size, it would be known as a square. From those two words, we get "rectangle".
Can't we assume they are rectangles, then?
 
lex said:
Yes, correct method and answer.

(A little note - you have used 'shaded region' in referring to the large rectangle and in referring to the actual s
Click to expand...
maybe I should have set it up this way
Area of non-shaded region = 90in^2
then do the subtraction
and then state,
the area of the region that is shaded is 64 in^2 after subtracting the one that was not shaded.
 
eddy2017 said:
but these are rectangles, aren't they?. they are not squares!

A rectangle is a 2D shape that has 4 sides, 4 corners, and 4 right angles. Opposite sides of a rectangle shape are the same length, with one pair being longer than the other pair. If all the sides of a rectangle were the same size, it would be known as a square. From those two words, we get "rectangle".
Can't we assume they are rectangles, then?
Click to expand...
I see no right angles at all:

1644095845111.png​

I imagine that in the book they look more like right angles than they do in your picture; and in such books you are often expected to make such assumptions knowing they wouldn't give you an impossible problem.

But a really good book would always tell you what to assume, and not make you guess based on what things look like! Math is not about assuming things without reason. That's a valid point!
 
lex said:
Yes, correct method and answer.

(A little note - you have used 'shaded region' in referring to the large rectangle and in referring to the actual shaded region).
Click to expand...
eddy2017 said:
I'm confused here. Isn't the shaded region that of the whole rectangle except for the area that occupies the white area (non-shaded)?
Click to expand...
Yes, assuming they are rectangles, your solution is correct, with the note I made earlier.
(They only gave the length and breadth of each shape, so I assume they meant these to be rectangles, and it was probably a reasonable assumption for you to make in solving it - you know the context, you know better than me then).
They should give all the information needed to solve the question, so they might either have stated they are rectangles or marked in right angles.
1644098244883.png
The danger in making assumptions is that sometimes they may be unwarranted!
 
My point is:

If particular ASSUMPTION/S are needed - those should be explicitly stated.
 
Dr.Peterson said:
I see no right angles at all:


I imagine that in the book they look more like right angles than they do in your picture; and in such books you are often expected to make such assumptions knowing they wouldn't give you an impossible problem.

But a really good book would always tell you what to assume, and not make you guess based on what things look like! Math is not about assuming things without reason. That's a valid point!
Click to expand...
I totally agree and it is like you say. They expect us to assume it and that is not correct.
 
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