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My answer is probably not correct because I'm like, the worst at geometry. :( But, I think I got the answer... First of all, since I know the area of the triangle is 210 cm squared, and the length is 30 cm, I use the triangle formula. To get the length of GD, I would have to multiply the area by 2 then divide it by 30, the length. The equation would be: 210*2/30=14. GD would be 14.
Now, I go on to the second clue, which says that the pentagon is 1000cm squared. Since I can't figure out that, I figure out the triangle that is missing to make this pentagon a rectangle. The base is 14, while the length is AB-CD. AB=50, and CD=15, so I subtract it and get 35. I use the triangle formula and I get an area of 245cm squared. So, I add it to 1000 and get 1245 cm square. Since the length of the now-made rectangle is 50, I divide 1245 by 50 and get the width of 24.9 cm. To figure out AE, I must use the width BC and subtract it by GD. 24.9-14=10.9. AE has the length of 10.9 cm. -Alan
I completed the Potw grade 8 question on paper and I got the answer that the hexagon is 300cm squared in area...I am not sure if it is completely correct but I did attempt the question.
I did not know how to approach this problem at first, but decided to make a few calculations, to see if that would get me anywhere.
First of all, I decided to calculate the length of the triangle's base, using the formula Area/Heightx2. I know the area is 210cm squared, and the height is 30, so I can add these into the formula.
210/30x2= 7x2= 14
Now that I know the length of side GD (14), I decided to make the pentagon into a rectangle, by taking the same triangle, but creating a copy of it and flipping it over. This would fit into the gap nicely.
Since I know the length of the rectangle (AB or 50 cm), and the area is calculated by multiplying the length by the width, I just have to solve this equation to find the width of the rectangle.
However, since I added the triangle, I need to add its area to the rectangle as well, which is 245. I figured this out using the formula 1/2 (bxh). Now, I can solve the equation.
50cm x y = 1245cm squared
I divided 1245 by 50, and got 24.9. I then double checked my answer using this formula.
50cm x 24.9cm = 1245cm squared
This worked, so I knew the width of the rectangle was 24.9 cm. I also knew that side GD, now a piece of the rectangle's width, was 14 cm. Since the only other piece was AE, I had to subtract 14 from 24.9 to get the length of AE.
First i started by writing down everything i know about the shape so far. However to make it easier to solve, I decided to draw a line through the shape. This way we have 2 different quadrilaterals. Then i moved onto the triangles. I knew that EF was 30 cm and i knew that the area of the triangle was 210cm. Then since I knew that in order to find the area of a triangle you need to do BxH/2. So I did the equation backwards to find out the length of GD. 210/30x2=14 This means that the length of GD is 14.As i mentioned earlier, i drew a line to make regular quadrilaterals. I continued the line down from EF all the way to the bottom. This was equal to AB which was 50 so i knew that my new line was also 50. But then I plugged in more numbers to try figure out the area of the other triangle (DFG). Then since i knew that my new line was 50, i just subtracted 2 other amounts to figure out the height of FG. I subtracted 15 and 30 (line CD and EF) from 50 and got 5. This meant that 5 was the height of FG. So now i could use my formula again. 5x14/2=35 This meant that the area of triangle DFG was 35 cm. Now i could take that number and further it into some calculations.
We knew that the area of the whole shape was 1000cm. Now since i split the shape into multiple other shapes this made these calculations much easier. I input all of the knowledge we had so far, into one large equation. 1000= ABxAE+GDxDC+FGxGD/2+210(area of the shaded triangle) Then i just started changing all the letters into numbers that I have figured out. 1000= 50xAE+14x15+5x14/2+210 After that i just did the simple equations i could while following BEDMAS. 1000= 50xAE+210+35+210 Now, I simplified even further. 1000= 50xAE+455 But now i came to a stopping point. I couldn't do any more equations because i had no idea what AE was. In order to figure that out, i subtracted 455 from out total of 1000. This meant that whatever number was leftover after this, would be equal to 50xAE. So i did as said. 1000-455 = 545 545= 50xAE So now comes the final part, where you simply divide these two numbers. I divided 545 by 50, in order to figure out 50x_=545. This gives us the final answer of 10.9.
I copied this image on Microsoft Paint and I put in all the lengths that I know. This includes AB (50 cm), EF (30 cm), CD (15 cm) and the areas of ABCDE (1000cm2) and EFD (210cm2). I found FG easily as all I had to do was subtract EF and DC from AB as lines EF, DC and FG add up to make AB (50 cm). 50-30-15=5. FG is 5 cm. I found EG after that as all I had to do was add EF and FG (20 + 5). I got 35 cm. EG is 35 cm.
If u flip triangle EGD, you would get a rectangle. I know that to find the area of a rectangle, I have to multiple L and W. I would have to divide the area by length or width to get the other. I need to find AE and it is equal to BC - GD. To find BC(W), I must divide the area of the rectangle by AB (L).
If EF is the base of triangle EFD, than GD is the height. The formula to find the area is B * H / 2 = A. If I want to find the height, the formula would be A * 2 / B = H. I can substitute that with 210 * 2 / 30. = 420 / 30. = 14. GD (H) is 14.
Now that I know what EG is, I can find the area of EGD. B * H / 2 35 * 14 / 2 = 490 / 2 = 245 The area of triangle EGD is 245 cm2.
Now I need to flip this to make a rectangle. By flipping this, I would be adding its area to the irregular pentagon (245 cm2 + 1000cm2). That gets me 1245 cm 2.
I know that 1 side of the rectangle is 50 cm so the other side would be 1245 / 50. That is equal to 24.9. BC is equal to 24.9 cm.
If I subtract GD from BC, I get AE. That is 24.9 - 14 which equals 10.9cm.
Here is how I went about solving the Grade 7 POTW #10: I first looked at the triangle and calculated the area of it. To find the area, you have to do (base * height) divided by 2. In triangle DEF, line EF is 30 cm long, and we can use line GD as another the base to make a perfect right triangle. Since it is given to us that the area of the triangle is 210 cm2, we can use that as the total and use 30 as one of the values. So we then divide 30 by 2 to give us a quotient of 15. After that, we divide 210 by 15 which gives us 14. So GD is equal to 14. Now we can refer back to the rules/boundaries that we were given. AB = 50 cm, CD = 15 cm, EF = 30 cm. Since area of the entire shape is 1000 cm2. In order to solve the question, I know that I have to fill-in the missing triangle and make the pentagon a rectangle. GD is equal to 14cm and the lengths are AB and CD. AB is equal to 15cm while CD is equal to 50. This means that we have to subtract it and 35 would be our difference. This allows us to find the area by doing (35 * 14) / 2 which equals 245 cm2. Then we add 1000 to 245 which sums up to 1245, and since the new length is 50, we divide 1245 by it and get 24.9 cm. Finally, to figure out AE, we take BC and subtract it by GD which looks like this: 24.9-14=10.9. Therefore, AE is 10.9 cm long.
Hey Luke, make sure you have a look at the question earlier in the week so that you can ask your peers and teachers for help, and also see their replies already up on the blog. Please have a look at the answer I've posted and how 10.9cm was obtained as the correct response.
POTW GRADE 7 Firstly, I figured the base of the triangle(The shaded area and the little triangle thing with the dashed lines) using the information it gave us. 210/30*2= 7*2= 14 I now know that GD (the base) is 14cm. Now I make the pentagon into a rectangle! (Beat that title C:< ) Using the formula, I subtract AB to CD. 50-15= 35 This is where GD comes into play, I insert 14 and 35 into the formula to figure out the area of a triangle and receive 245. So now, I add 245 and 1000 because I added a new area to the area. 1000+245=1245 After than, I evaluate 1245/50= 24.9 Then I use what is now BC, subtract it by GD and... BOOM! 10.9 So, in a FULL SENTENCE, AE is equal to 10.9.
My answer is probably not correct because I'm like, the worst at geometry. :(
ReplyDeleteBut, I think I got the answer...
First of all, since I know the area of the triangle is 210 cm squared, and the length is 30 cm, I use the triangle formula. To get the length of GD, I would have to multiply the area by 2 then divide it by 30, the length.
The equation would be:
210*2/30=14. GD would be 14.
Now, I go on to the second clue, which says that the pentagon is 1000cm squared. Since I can't figure out that, I figure out the triangle that is missing to make this pentagon a rectangle. The base is 14, while the length is AB-CD. AB=50, and CD=15, so I subtract it and get 35. I use the triangle formula and I get an area of 245cm squared. So, I add it to 1000 and get 1245 cm square. Since the length of the now-made rectangle is 50, I divide 1245 by 50 and get the width of 24.9 cm. To figure out AE, I must use the width BC and subtract it by GD. 24.9-14=10.9. AE has the length of 10.9 cm.
-Alan
AE has the length of 10.9 cm. I completed my explanation on paper.
ReplyDeleteThe length of the lines from 10.9 cm. My work is on my math book.
ReplyDeleteI completed the Potw grade 8 question on paper and I got the answer that the hexagon is 300cm squared in area...I am not sure if it is completely correct but I did attempt the question.
ReplyDeleteI did not know how to approach this problem at first, but decided to make a few calculations, to see if that would get me anywhere.
ReplyDeleteFirst of all, I decided to calculate the length of the triangle's base, using the formula Area/Heightx2. I know the area is 210cm squared, and the height is 30, so I can add these into the formula.
210/30x2=
7x2=
14
Now that I know the length of side GD (14), I decided to make the pentagon into a rectangle, by taking the same triangle, but creating a copy of it and flipping it over. This would fit into the gap nicely.
Since I know the length of the rectangle (AB or 50 cm), and the area is calculated by multiplying the length by the width, I just have to solve this equation to find the width of the rectangle.
However, since I added the triangle, I need to add its area to the rectangle as well, which is 245. I figured this out using the formula 1/2 (bxh). Now, I can solve the equation.
50cm x y = 1245cm squared
I divided 1245 by 50, and got 24.9. I then double checked my answer using this formula.
50cm x 24.9cm = 1245cm squared
This worked, so I knew the width of the rectangle was 24.9 cm. I also knew that side GD, now a piece of the rectangle's width, was 14 cm. Since the only other piece was AE, I had to subtract 14 from 24.9 to get the length of AE.
24.9-14= 10.9
Therefore, the length of line AE is 10.9 cm
The length of the line AE is 10.9 cm. My work is in my 1st math book which seems to have escaped from my presence. I'm looking for it right now :P
ReplyDeleteThe Length of the line AE is 10.9 cm.
ReplyDeleteFirst i started by writing down everything i know about the shape so far. However to make it easier to solve, I decided to draw a line through the shape. This way we have 2 different quadrilaterals. Then i moved onto the triangles. I knew that EF was 30 cm and i knew that the area of the triangle was 210cm. Then since I knew that in order to find the area of a triangle you need to do BxH/2. So I did the equation backwards to find out the length of GD.
210/30x2=14
This means that the length of GD is 14.As i mentioned earlier, i drew a line to make regular quadrilaterals. I continued the line down from EF all the way to the bottom. This was equal to AB which was 50 so i knew that my new line was also 50. But then I plugged in more numbers to try figure out the area of the other triangle (DFG). Then since i knew that my new line was 50, i just subtracted 2 other amounts to figure out the height of FG. I subtracted 15 and 30 (line CD and EF) from 50 and got 5. This meant that 5 was the height of FG. So now i could use my formula again.
5x14/2=35
This meant that the area of triangle DFG was 35 cm. Now i could take that number and further it into some calculations.
We knew that the area of the whole shape was 1000cm. Now since i split the shape into multiple other shapes this made these calculations much easier. I input all of the knowledge we had so far, into one large equation.
1000= ABxAE+GDxDC+FGxGD/2+210(area of the shaded triangle)
Then i just started changing all the letters into numbers that I have figured out.
1000= 50xAE+14x15+5x14/2+210
After that i just did the simple equations i could while following BEDMAS.
1000= 50xAE+210+35+210
Now, I simplified even further.
1000= 50xAE+455
But now i came to a stopping point. I couldn't do any more equations because i had no idea what AE was. In order to figure that out, i subtracted 455 from out total of 1000. This meant that whatever number was leftover after this, would be equal to 50xAE. So i did as said.
1000-455 = 545
545= 50xAE
So now comes the final part, where you simply divide these two numbers. I divided 545 by 50, in order to figure out 50x_=545. This gives us the final answer of 10.9.
I copied this image on Microsoft Paint and I put in all the lengths that I know. This includes AB (50 cm), EF (30 cm), CD (15 cm) and the areas of ABCDE (1000cm2) and EFD (210cm2).
ReplyDeleteI found FG easily as all I had to do was subtract EF and DC from AB as lines EF, DC and FG add up to make AB (50 cm). 50-30-15=5. FG is 5 cm.
I found EG after that as all I had to do was add EF and FG (20 + 5). I got 35 cm. EG is 35 cm.
If u flip triangle EGD, you would get a rectangle. I know that to find the area of a rectangle, I have to multiple L and W. I would have to divide the area by length or width to get the other. I need to find AE and it is equal to BC - GD. To find BC(W), I must divide the area of the rectangle by AB (L).
If EF is the base of triangle EFD, than GD is the height. The formula to find the area is B * H / 2 = A. If I want to find the height, the formula would be A * 2 / B = H.
I can substitute that with
210 * 2 / 30.
= 420 / 30.
= 14.
GD (H) is 14.
Now that I know what EG is, I can find the area of EGD.
B * H / 2
35 * 14 / 2
= 490 / 2
= 245
The area of triangle EGD is 245 cm2.
Now I need to flip this to make a rectangle. By flipping this, I would be adding its area to the irregular pentagon (245 cm2 + 1000cm2). That gets me 1245 cm 2.
I know that 1 side of the rectangle is 50 cm so the other side would be
1245 / 50. That is equal to 24.9.
BC is equal to 24.9 cm.
If I subtract GD from BC, I get AE. That is 24.9 - 14 which equals 10.9cm.
The length of AE is 10.9.
Here is how I went about solving the Grade 7 POTW #10:
ReplyDeleteI first looked at the triangle and calculated the area of it. To find the area, you have to do (base * height) divided by 2. In triangle DEF, line EF is 30 cm long, and we can use line GD as another the base to make a perfect right triangle. Since it is given to us that the area of the triangle is 210 cm2, we can use that as the total and use 30 as one of the values. So we then divide 30 by 2 to give us a quotient of 15. After that, we divide 210 by 15 which gives us 14. So GD is equal to 14. Now we can refer back to the rules/boundaries that we were given. AB = 50 cm, CD = 15 cm, EF = 30 cm. Since area of the entire shape is 1000 cm2. In order to solve the question, I know that I have to fill-in the missing triangle and make the pentagon a rectangle. GD is equal to 14cm and the lengths are AB and CD. AB is equal to 15cm while CD is equal to 50. This means that we have to subtract it and 35 would be our difference. This allows us to find the area by doing (35 * 14) / 2 which equals 245 cm2. Then we add 1000 to 245 which sums up to 1245, and since the new length is 50, we divide 1245 by it and get 24.9 cm. Finally, to figure out AE, we take BC and subtract it by GD which looks like this: 24.9-14=10.9. Therefore, AE is 10.9 cm long.
Me and both my parents attempted this. We plugged in a lot of numbers but, were unable to solve it. I will bring in the sheet tommorow.
ReplyDeleteHey Luke, make sure you have a look at the question earlier in the week so that you can ask your peers and teachers for help, and also see their replies already up on the blog. Please have a look at the answer I've posted and how 10.9cm was obtained as the correct response.
DeletePOTW GRADE 7
ReplyDeleteFirstly, I figured the base of the triangle(The shaded area and the little triangle thing with the dashed lines) using the information it gave us.
210/30*2=
7*2=
14
I now know that GD (the base) is 14cm.
Now I make the pentagon into a rectangle! (Beat that title C:< )
Using the formula, I subtract AB to CD.
50-15=
35
This is where GD comes into play, I insert 14 and 35 into the formula to figure out the area of a triangle and receive 245.
So now, I add 245 and 1000 because I added a new area to the area.
1000+245=1245
After than, I evaluate
1245/50=
24.9
Then I use what is now BC, subtract it by GD and...
BOOM!
10.9
So, in a FULL SENTENCE, AE is equal to 10.9.
I LOVE the POTW #10 Gr. 7 question by the way. Do you see how and why it is 10.9cm? So many steps and what an elaborate problem!
ReplyDeleteSorry for the late response, but I got an answer of 237.5cm2
ReplyDelete