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Before I answer the question, i am wondering is it the ratio of the total amount of unshaded area added all together and the total amount of shaded area added all together or just the amount that contain white triangles and plain shaded?
Ok i'm assuming it is the first option.
So what i think is to first calculate the area of the top left corner. when i look at it, i can see i can put pieces together to make a whole (i would show you but i can't so i will just explain it using coordinates A B C D E 5 4 3 2 1 so when i look at B5, i see that on the, non shaded, one edge is split in half so i can make it into a half by adding B4 because it fits if you flip it upsidedown. that is half. then i also notice that C4 can fit into A5 making it a half. if you added it together you get 1cm squared.
On the top right, E5 is half so that is easy. D4 looks like it can be formed into a half also so D5 can be rotated a couple times to make it fit into D4. One half + one half = 1 cm squared
For the bottom left, there is already one whole(A1). B2 looks like it can fit B3 and C2 so that is also one. This next part was hard for me to find. i look at C3 and rotate it so it would fit into A2 and also space for B2. All that would equal 3cm squared
For the last one, I see a full 1 1/2. As i look, i notice that D4 can be made into a half by adding D1. so now there is one left, D2. i noticed that it is half of the square. so added together and it was 2.5cm squared.
I added all the totals and got 7.5cm squared. I know that there are 25 squares so i did 25-7.5 to find what is shaded. it was 17.5cm squared.
The ratio is 17.5 : 7.5
well that is the answer. this is probably confusing so if you are wondering what i am trying to say please come ask because i am terrible at explaining things in words. :)
Hi. My brother and I answered this question together.
The ratio that we found is 33:17
To find this answer we used several different math strategies (finding the area of a triangle/subtraction/addition/multiplication). First, we determined the area of the shaded section as opposed to the unshaded section because we thought it would be simpler this way. My brother and I labeled the different shaded areas A1, A2, A3, A4. The top = A1, the right = A2, the bottom = A3, the left = A4
We found the area of each shaded section by using the formula to find the area of a triangle (Base x Height / 2).
After finding the area of each section, we added it all together (A1 + A2 + A3 + A4). The total we found was 16.5 cm2. Then we subtracted the total (25) by the subtotal (16.5) and got 8.5, which means the area of the unshaded section is 8.5cm2
So then the ratio of the shaded area to the unshaded area is 16.5:8.5. By multiplying it by 2 to make it a whole number, it will make it 33:17.
hello So what i did was organize the parts that aren't shaded together to make wholes. kind of like fractions. I would describe how but that would take to long.
Anyway, the top left comes out to be 1 square. the top right comes out to be also 1 square The bottom left came out to be 3 square And lastly the bottom right is 2.5 square
I added them together and i got 7.5 squares
So i know that there are 25 squares in total so that means there are 17.5 squares that are shaded. {i did 25 - 7.5}
So now i know that the ratio of shaded area to unshaded area is 17.5 : 7.5 squares.
you guys both did great! Rachel and Jon you might want to check your calculation (re: shaded area total; since i got 17.5 instead of 16.5); Sophia: have you considered simplifying the ratio? (divided by 2.5 for each term)
Before I answer the question, i am wondering is it the ratio of the total amount of unshaded area added all together and the total amount of shaded area added all together or just the amount that contain white triangles and plain shaded?
ReplyDeleteOk i'm assuming it is the first option.
So what i think is to first calculate the area of the top left corner. when i look at it, i can see i can put pieces together to make a whole (i would show you but i can't so i will just explain it using coordinates
A B C D E
5
4
3
2
1
so when i look at B5, i see that on the, non shaded, one edge is split in half so i can make it into a half by adding B4 because it fits if you flip it upsidedown. that is half. then i also notice that C4 can fit into A5 making it a half. if you added it together you get 1cm squared.
On the top right, E5 is half so that is easy. D4 looks like it can be formed into a half also so D5 can be rotated a couple times to make it fit into D4. One half + one half = 1 cm squared
For the bottom left, there is already one whole(A1). B2 looks like it can fit B3 and C2 so that is also one. This next part was hard for me to find. i look at C3 and rotate it so it would fit into A2 and also space for B2. All that would equal 3cm squared
For the last one, I see a full 1 1/2. As i look, i notice that D4 can be made into a half by adding D1. so now there is one left, D2. i noticed that it is half of the square. so added together and it was 2.5cm squared.
I added all the totals and got 7.5cm squared. I know that there are 25 squares so i did 25-7.5 to find what is shaded. it was 17.5cm squared.
The ratio is 17.5 : 7.5
well that is the answer. this is probably confusing so if you are wondering what i am trying to say please come ask because i am terrible at explaining things in words. :)
Hi. My brother and I answered this question together.
ReplyDeleteThe ratio that we found is 33:17
To find this answer we used several different math strategies (finding the area of a triangle/subtraction/addition/multiplication).
First, we determined the area of the shaded section as opposed to the unshaded section because we thought it would be simpler this way.
My brother and I labeled the different shaded areas A1, A2, A3, A4. The top = A1, the right = A2, the bottom = A3, the left = A4
We found the area of each shaded section by using the formula to find the area of a triangle (Base x Height / 2).
After finding the area of each section, we added it all together (A1 + A2 + A3 + A4). The total we found was 16.5 cm2. Then we subtracted the total (25) by the subtotal (16.5) and got 8.5, which means the area of the unshaded section is 8.5cm2
So then the ratio of the shaded area to the unshaded area is 16.5:8.5. By multiplying it by 2 to make it a whole number, it will make it 33:17.
- Rachel and Jonathan
hello
ReplyDeleteSo what i did was organize the parts that aren't shaded together to make wholes. kind of like fractions. I would describe how but that would take to long.
Anyway, the top left comes out to be 1 square.
the top right comes out to be also 1 square
The bottom left came out to be 3 square
And lastly the bottom right is 2.5 square
I added them together and i got 7.5 squares
So i know that there are 25 squares in total so that means there are 17.5 squares that are shaded. {i did 25 - 7.5}
So now i know that the ratio of shaded area to unshaded area is 17.5 : 7.5 squares.
Hopefully you understand and bye!! :D
hi guys
ReplyDeleteyou guys both did great! Rachel and Jon you might want to check your calculation (re: shaded area total; since i got 17.5 instead of 16.5); Sophia: have you considered simplifying the ratio? (divided by 2.5 for each term)
great explanation!