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POTW: - 4 strips of wood: 30 x 3 each - Find the area
Basically what this problem is asking is what is the area of the inside frame without the thickness of the strips. So, what we have to do it find the area of the whole figure, minus the area of the frame itself. What isn't a problem though, is the way the frame is arranged. Since each piece has one adjacent piece overlapping it, and one right next to it, they both cancel out and the measurements are still the same. However, if this frame was arranged in a way that the bottom piece "holds" two other pieces on top, problems (ish) would occur, but since that is not the case here, we can just ignore that. To find the total area of the region avec le frame (hehe french), we can take the length x width. A= l x w A= 30 x 30 A= 30^2 A= 900 The total area is 900 cm^2. To find the area of the frame, we take the length and width of the frame and multiply that by 4 to find the total area. Then we can subtract that from the total area including the inside region. (Af= Area frame) Af= l x w x 4 Af= 30 x 3 x 4 Af: 360 Now we can subtract. (At= Area total) At= A- Af At= 900-360 A= 540 The total area of the region inside the frame is 540 cm^2.
Oh no, after looking closer at the frame, I realized that there was indeed an extra 3 cm added onto the frame (oopsiessssssssss ehehhehehehehehee). Anyways, the total are would be 33 x 33= 1089 and after I subtract 360, I get 729 cm^2 yay
Grade 7/8 POTW What we have to do is find the area of the region inside the picture frame. The picture frame is made up of 4 pieces of wood. Each piece is 30 x 3 cm. There are 2 ways in which we can solve this problem. We can either calculate the actual area individually, or calculate the entire area of the frame and the area and subtract the frame. First, we'll have to find the dimensions of both. The 4 pieces of wood would (homophones) be arranged in a way so that the first piece of wood would be normal, the next would be beside rotated 90 degrees, adding 3 cm to the length, and continuing around the perimeter like that until it creates a square. After this is done, the dimensions of the outer frame would be 33 by 33 while the dimension of the actual space would be 27 x 27. This is because as you can see, 3 cm is being cut off from the 30 cm long wood. 30 - 3 = 27. Anyways, for the first option, you can find the area by doing the formula l^2 or l x l or l x w. In other terms 27 x 27 = 729 cm^2. This is the first way. The second way is by finding the entire area and then subtracting the wood area. The same formula is used. 33 x 33 = 1089. 30 x 3 = 90. 90 x 4 = 360. 1089 - 360 = 729. Both gives us the same answer which further proves this. Therefore, the area of the region inside of the frame is 729 cm^2.
There is a short and simple shortcut concerning this question. Each strip is 30 CM long, and each strip is overlapped by 1 that is 3 cm wide. 30-3=27, and doing this with each of the sides forms a square with each side being 27cm. (pay close attention to the picture!)
Now 27^2 is 729 cm^2, and that means 729 square centimetres is probably the answer!
(if it's not I didn't look close enough at that frame)
Area of whole frame - area of wood strips = area of the inside of the frame. First I found the area of the whole frame- 30 x 30 = 900. Then I calculated the area of the wooden strips (since there are strips of wood on all 4 sides of the frame, this means that they overlap, meaning that the length of the strips is not 30 but, 27). L x W x 4 = Area of the 4 strips. 27 x 3 x 4 = 324. Finally I subtracted 324cm^2 from 900cm^2 and it equaled to 576cm^2.
Therefor the area of the inside of the fame is 576cm^2.
Grade 7/8 POTW The answer to this question is actually very simple. There are 2 ways to complete this question. The first is to find the area of the inside of the picture frame which means eliminating the total area of each of the pieces of wood to the total area of the picture. 3x30x4=360 - this equation sums up all of the pieces of wood. 33x33= 1089 - this is the total area of the pieces of wood and the area inside of the wood. 1089-360= 729 cm squared - this the area of the picture frame.
The next and even more simple way to do this is to just find the length and width of each side inside the wood planks and multiply them. Length= 27 cm Width= 27 cm 27x27= 729 cm squared.
The total are of the region inside the frame is 729 cm squared.
30x3 for each strip of wood, so if you were to subtract the width from the length it would be 27 which would be the length and with of the inner rectangle. so then to find the area you do 27x27=792 cm squared
Old Length= 30 Old Width= 30 Old Area=30x30 =900 New Length=30-3 =27 New Width=30-3 =27 New Area=27x27 =729
The way the wood is placed each side is now 33cm. 33cm x 33cm = 1089cm2 (area) 33cm x 4(# of sides) = 132cm (perimeter)
If we subtract the 3 extra cm and take away 3 more cm from the 33cm than we have 27cm. If we do the same equation with 27cm we will get the answer. 27cm x 27cm = 729cm2 (new area) 27cm x 4(# of sides) = 108cm (new perimeter)
Therefore 729cm2 is the area of within the frame. Also the perimeter is 108cm.
Grade 7/8 POTW (Maryam) First, I subtracted 3 cm from the frame since the frame is 3 cm wide and I only need to find the area of the region inside the frame. 30 - 3 = 27 cm After that, I used the formula for the area of a rectangle (LxW) to find the area A= LxW A= 27 x 27 A= 729 The area of the region inside the frame is 729 cm.
Find the length and width of the inside square. Since the wood is 3cm thick you need to subtract it from the length as it overlaps. 30-3=27 27² = 27*27 = 729
First you figure the inside lengths which you get 30 cm and subtract 3 cm because if you see the picture each length of the strip which is 30 cm has one part covered by the width which is 3 cm. This gets you 27 which then you square to get an inside region of 729cm2.
First you figure the inside lengths which you get 30 cm and subtract 3 cm because if you see the picture each length of the strip which is 30 cm has one part covered by the width which is 3 cm. This gets you 27 which then you square to get an inside region of 729cm2.
The total area of the frame is 900 cm squared. However, since the sides of the wood frame are overlapping, you would need to subtract the amount that is covered: 30 - 3 = 27. (3 is subtracted because the frame is 3 cm wide). 27 x 27 = 729 cm squared
To find the area of the inner square, (the empty space) I am going to subtract 3 cm from each of the 30 cm (the length of the wood) so I only calculate the inside. 30 cm minus 3 cm equals 27, so I just use that instead of 30 cm. Area= LxW= 27x27= 729 cm2 The area is 729 cm2
This frame is in the shape of square, so to find the are we would multiply the base by height (b*h=a). Since the outside of the frame is 30 cm each, we would do 30 cm*30 cm, which equals 900 cm2. The width of each strip is 3 cm, and each strip is overlapping from one side. So, to find the length of each side inside the frame, we would do 30 cm -3 cm, which equals 27 cm. Now, to find the area inside the frame, we would do 27 cm* 27 cm, which would equal 729 cm2.
POTW:
ReplyDelete- 4 strips of wood: 30 x 3 each
- Find the area
Basically what this problem is asking is what is the area of the inside frame without the thickness of the strips. So, what we have to do it find the area of the whole figure, minus the area of the frame itself. What isn't a problem though, is the way the frame is arranged. Since each piece has one adjacent piece overlapping it, and one right next to it, they both cancel out and the measurements are still the same. However, if this frame was arranged in a way that the bottom piece "holds" two other pieces on top, problems (ish) would occur, but since that is not the case here, we can just ignore that. To find the total area of the region avec le frame (hehe french), we can take the length x width.
A= l x w
A= 30 x 30
A= 30^2
A= 900
The total area is 900 cm^2.
To find the area of the frame, we take the length and width of the frame and multiply that by 4 to find the total area. Then we can subtract that from the total area including the inside region.
(Af= Area frame)
Af= l x w x 4
Af= 30 x 3 x 4
Af: 360
Now we can subtract.
(At= Area total)
At= A- Af
At= 900-360
A= 540
The total area of the region inside the frame is 540 cm^2.
Oh no, after looking closer at the frame, I realized that there was indeed an extra 3 cm added onto the frame (oopsiessssssssss ehehhehehehehehee). Anyways, the total are would be 33 x 33= 1089 and after I subtract 360, I get 729 cm^2 yay
DeleteGrade 7/8 POTW
ReplyDeleteWhat we have to do is find the area of the region inside the picture frame. The picture frame is made up of 4 pieces of wood. Each piece is 30 x 3 cm. There are 2 ways in which we can solve this problem. We can either calculate the actual area individually, or calculate the entire area of the frame and the area and subtract the frame. First, we'll have to find the dimensions of both. The 4 pieces of wood would (homophones) be arranged in a way so that the first piece of wood would be normal, the next would be beside rotated 90 degrees, adding 3 cm to the length, and continuing around the perimeter like that until it creates a square. After this is done, the dimensions of the outer frame would be 33 by 33 while the dimension of the actual space would be 27 x 27. This is because as you can see, 3 cm is being cut off from the 30 cm long wood. 30 - 3 = 27. Anyways, for the first option, you can find the area by doing the formula l^2 or l x l or l x w. In other terms 27 x 27 = 729 cm^2. This is the first way. The second way is by finding the entire area and then subtracting the wood area. The same formula is used. 33 x 33 = 1089. 30 x 3 = 90. 90 x 4 = 360. 1089 - 360 = 729. Both gives us the same answer which further proves this.
Therefore, the area of the region inside of the frame is 729 cm^2.
There is a short and simple shortcut concerning this question. Each strip is 30 CM long, and each strip is overlapped by 1 that is 3 cm wide. 30-3=27, and doing this with each of the sides forms a square with each side being 27cm. (pay close attention to the picture!)
ReplyDeleteNow 27^2 is 729 cm^2, and that means 729 square centimetres is probably the answer!
(if it's not I didn't look close enough at that frame)
POTW Grade - 7/8
ReplyDeleteArea of whole frame - area of wood strips = area of the inside of the frame.
First I found the area of the whole frame- 30 x 30 = 900.
Then I calculated the area of the wooden strips (since there are strips of wood on all 4 sides of the frame, this means that they overlap, meaning that the length of the strips is not 30 but, 27). L x W x 4 = Area of the 4 strips. 27 x 3 x 4 = 324.
Finally I subtracted 324cm^2 from 900cm^2 and it equaled to 576cm^2.
Therefor the area of the inside of the fame is 576cm^2.
Grade 7/8 POTW
ReplyDeleteThe answer to this question is actually very simple. There are 2 ways to complete this question.
The first is to find the area of the inside of the picture frame which means eliminating the total area of each of the pieces of wood to the total area of the picture.
3x30x4=360 - this equation sums up all of the pieces of wood.
33x33= 1089 - this is the total area of the pieces of wood and the area inside of the wood.
1089-360= 729 cm squared - this the area of the picture frame.
The next and even more simple way to do this is to just find the length and width of each side inside the wood planks and multiply them.
Length= 27 cm
Width= 27 cm
27x27= 729 cm squared.
The total are of the region inside the frame is 729 cm squared.
30x3 for each strip of wood, so if you were to subtract the width from the length it would be 27 which would be the length and with of the inner rectangle. so then to find the area you do 27x27=792 cm squared
ReplyDeleteOld Length= 30
Old Width= 30
Old Area=30x30
=900
New Length=30-3
=27
New Width=30-3
=27
New Area=27x27
=729
Aliyah
ReplyDeleteThe way the wood is placed each side is now 33cm.
33cm x 33cm = 1089cm2 (area)
33cm x 4(# of sides) = 132cm (perimeter)
If we subtract the 3 extra cm and take away 3 more cm from the 33cm than we have 27cm. If we do the same equation with 27cm we will get the answer.
27cm x 27cm = 729cm2 (new area)
27cm x 4(# of sides) = 108cm (new perimeter)
Therefore 729cm2 is the area of within the frame. Also the perimeter is 108cm.
To solve this problem you take the area of the whole (33x33) and subtract the area of the frame (30x3x4) to get the total area
ReplyDeleteso:
33x33 = 1089
30x3x4 = 360
1089-395 = 729 therefore the area of the inside is 729
Grade 7/8 POTW (Maryam)
ReplyDeleteFirst, I subtracted 3 cm from the frame since the frame is 3 cm wide and I only need to find the area of the region inside the frame.
30 - 3 = 27 cm
After that, I used the formula for the area of a rectangle (LxW) to find the area
A= LxW
A= 27 x 27
A= 729
The area of the region inside the frame is 729 cm.
Find the length and width of the inside square. Since the wood is 3cm thick you need to subtract it from the length as it overlaps.
ReplyDelete30-3=27
27² = 27*27 = 729
First you figure the inside lengths which you get 30 cm and subtract 3 cm because if you see the picture each length of the strip which is 30 cm has one part covered by the width which is 3 cm. This gets you 27 which then you square to get an inside region of 729cm2.
ReplyDeleteFirst you figure the inside lengths which you get 30 cm and subtract 3 cm because if you see the picture each length of the strip which is 30 cm has one part covered by the width which is 3 cm. This gets you 27 which then you square to get an inside region of 729cm2.
ReplyDeletePOTW:
ReplyDeleteThe total area of the frame is 900 cm squared.
However, since the sides of the wood frame are overlapping, you would need to subtract the amount that is covered: 30 - 3 = 27. (3 is subtracted because the frame is 3 cm wide).
27 x 27 = 729 cm squared
To find the area of the inner square, (the empty space) I am going to subtract 3 cm from each of the 30 cm (the length of the wood) so I only calculate the inside. 30 cm minus 3 cm equals 27, so I just use that instead of 30 cm.
ReplyDeleteArea= LxW=
27x27=
729 cm2
The area is 729 cm2
This frame is in the shape of square, so to find the are we would multiply the base by height (b*h=a). Since the outside of the frame is 30 cm each, we would do 30 cm*30 cm, which equals 900 cm2. The width of each strip is 3 cm, and each strip is overlapping from one side. So, to find the length of each side inside the frame, we would do 30 cm -3 cm, which equals 27 cm. Now, to find the area inside the frame, we would do 27 cm* 27 cm, which would equal 729 cm2.
ReplyDelete